diff --git a/expression/builtin_time.go b/expression/builtin_time.go
index 62a8107a48da1..45ef659976f09 100644
--- a/expression/builtin_time.go
+++ b/expression/builtin_time.go
@@ -1572,26 +1572,30 @@ func (c *fromUnixTimeFunctionClass) getFunction(ctx sessionctx.Context, args []E
 	_, isArg0Con := args[0].(*Constant)
 	isArg0Str := args[0].GetType().EvalType() == types.ETString
 	bf := newBaseBuiltinFuncWithTp(ctx, args, retTp, argTps...)
-	if len(args) == 1 {
-		if isArg0Str {
-			bf.tp.Decimal = types.MaxFsp
-		} else if isArg0Con {
-			arg0, _, err1 := args[0].EvalDecimal(ctx, chunk.Row{})
-			if err1 != nil {
-				return sig, err1
-			}
+
+	if len(args) > 1 {
+		bf.tp.Flen = args[1].GetType().Flen
+		return &builtinFromUnixTime2ArgSig{bf}, nil
+	}
+
+	// Calculate the time fsp.
+	switch {
+	case isArg0Str:
+		bf.tp.Decimal = int(types.MaxFsp)
+	case isArg0Con:
+		arg0, arg0IsNull, err0 := args[0].EvalDecimal(ctx, chunk.Row{})
+		if err0 != nil {
+			return nil, err0
+		}
+
+		bf.tp.Decimal = int(types.MaxFsp)
+		if !arg0IsNull {
 			fsp := int(arg0.GetDigitsFrac())
-			if fsp > types.MaxFsp {
-				fsp = types.MaxFsp
-			}
-			bf.tp.Decimal = fsp
+			bf.tp.Decimal = mathutil.Min(fsp, int(types.MaxFsp))
 		}
-		sig = &builtinFromUnixTime1ArgSig{bf}
-	} else {
-		bf.tp.Flen = args[1].GetType().Flen
-		sig = &builtinFromUnixTime2ArgSig{bf}
 	}
-	return sig, nil
+
+	return &builtinFromUnixTime1ArgSig{bf}, nil
 }
 
 func evalFromUnixTime(ctx sessionctx.Context, fsp int, row chunk.Row, arg Expression) (res types.Time, isNull bool, err error) {
diff --git a/planner/core/integration_test.go b/planner/core/integration_test.go
index ff7ca01e6dd92..21f2ad151f7c5 100644
--- a/planner/core/integration_test.go
+++ b/planner/core/integration_test.go
@@ -15,22 +15,44 @@ package core_test
 
 import (
 	. "github.com/pingcap/check"
+	"github.com/pingcap/tidb/domain"
+	"github.com/pingcap/tidb/kv"
 	"github.com/pingcap/tidb/util/testkit"
+	"github.com/pingcap/tidb/util/testutil"
 )
 
 var _ = Suite(&testIntegrationSuite{})
 
 type testIntegrationSuite struct {
+	testData testutil.TestData
+	store    kv.Storage
+	dom      *domain.Domain
 }
 
-func (s *testIntegrationSuite) TestShowSubquery(c *C) {
-	store, dom, err := newStoreWithBootstrap()
+func (s *testIntegrationSuite) SetUpSuite(c *C) {
+	var err error
+	s.testData, err = testutil.LoadTestSuiteData("testdata", "integration_suite")
+	c.Assert(err, IsNil)
+}
+
+func (s *testIntegrationSuite) TearDownSuite(c *C) {
+	c.Assert(s.testData.GenerateOutputIfNeeded(), IsNil)
+}
+
+func (s *testIntegrationSuite) SetUpTest(c *C) {
+	var err error
+	s.store, s.dom, err = newStoreWithBootstrap()
+	c.Assert(err, IsNil)
+}
+
+func (s *testIntegrationSuite) TearDownTest(c *C) {
+	s.dom.Close()
+	err := s.store.Close()
 	c.Assert(err, IsNil)
-	tk := testkit.NewTestKit(c, store)
-	defer func() {
-		dom.Close()
-		store.Close()
-	}()
+}
+
+func (s *testIntegrationSuite) TestShowSubquery(c *C) {
+	tk := testkit.NewTestKit(c, s.store)
 	tk.MustExec("use test")
 	tk.MustExec("drop table if exists t")
 	tk.MustExec("create table t(a varchar(10), b int, c int)")
@@ -59,3 +81,27 @@ func (s *testIntegrationSuite) TestShowSubquery(c *C) {
 		"a varchar(10) YES  <nil> ",
 	))
 }
+
+func (s *testIntegrationSuite) TestIsFromUnixtimeNullRejective(c *C) {
+	tk := testkit.NewTestKit(c, s.store)
+	tk.MustExec("use test")
+	tk.MustExec(`drop table if exists t;`)
+	tk.MustExec(`create table t(a bigint, b bigint);`)
+	s.runTestsWithTestData("TestIsFromUnixtimeNullRejective", tk, c)
+}
+
+func (s *testIntegrationSuite) runTestsWithTestData(caseName string, tk *testkit.TestKit, c *C) {
+	var input []string
+	var output []struct {
+		SQL  string
+		Plan []string
+	}
+	s.testData.GetTestCasesByName(caseName, c, &input, &output)
+	for i, tt := range input {
+		s.testData.OnRecord(func() {
+			output[i].SQL = tt
+			output[i].Plan = s.testData.ConvertRowsToStrings(tk.MustQuery(tt).Rows())
+		})
+		tk.MustQuery(tt).Check(testkit.Rows(output[i].Plan...))
+	}
+}
diff --git a/planner/core/testdata/integration_suite_in.json b/planner/core/testdata/integration_suite_in.json
new file mode 100644
index 0000000000000..a4722af040a71
--- /dev/null
+++ b/planner/core/testdata/integration_suite_in.json
@@ -0,0 +1,22 @@
+[
+  {
+    "name": "TestPushLimitDownIndexLookUpReader",
+    "cases": [
+      // Limit should be pushed down into IndexLookUpReader, row count of IndexLookUpReader and TableScan should be 1.00.
+      "explain select * from tbl use index(idx_b_c) where b > 1 limit 2,1",
+	  // Projection atop IndexLookUpReader, Limit should be pushed down into IndexLookUpReader, and Projection should have row count 1.00 as well.
+      "explain select * from tbl use index(idx_b_c) where b > 1 order by b desc limit 2,1",
+	  // Limit should be pushed down into IndexLookUpReader when Selection on top of IndexScan.
+	  "explain select * from tbl use index(idx_b_c) where b > 1 and c > 1 limit 2,1",
+	  // Limit should NOT be pushed down into IndexLookUpReader when Selection on top of TableScan.
+	  "explain select * from tbl use index(idx_b_c) where b > 1 and a > 1 limit 2,1"
+    ]
+  },
+  {
+    "name": "TestIsFromUnixtimeNullRejective",
+    "cases": [
+      // fix #12385
+      "explain select * from t t1 left join t t2 on t1.a=t2.a where from_unixtime(t2.b);"
+    ]
+  }
+]
diff --git a/planner/core/testdata/integration_suite_out.json b/planner/core/testdata/integration_suite_out.json
new file mode 100644
index 0000000000000..0b256fd7aa314
--- /dev/null
+++ b/planner/core/testdata/integration_suite_out.json
@@ -0,0 +1,24 @@
+[
+  {
+    "Name": "TestPushLimitDownIndexLookUpReader",
+    "Cases": null
+  },
+  {
+    "Name": "TestIsFromUnixtimeNullRejective",
+    "Cases": [
+      {
+        "SQL": "explain select * from t t1 left join t t2 on t1.a=t2.a where from_unixtime(t2.b);",
+        "Plan": [
+          "HashLeftJoin_8 9990.00 root inner join, inner:Selection_13, equal:[eq(test.t1.a, test.t2.a)]",
+          "├─TableReader_12 9990.00 root data:Selection_11",
+          "│ └─Selection_11 9990.00 cop not(isnull(test.t1.a))",
+          "│   └─TableScan_10 10000.00 cop table:t1, range:[-inf,+inf], keep order:false, stats:pseudo",
+          "└─Selection_13 7992.00 root from_unixtime(cast(test.t2.b))",
+          "  └─TableReader_16 9990.00 root data:Selection_15",
+          "    └─Selection_15 9990.00 cop not(isnull(test.t2.a))",
+          "      └─TableScan_14 10000.00 cop table:t2, range:[-inf,+inf], keep order:false, stats:pseudo"
+        ]
+      }
+    ]
+  }
+]
diff --git a/util/testutil/testutil.go b/util/testutil/testutil.go
index c89d841a2b2c5..9e4928c6df696 100644
--- a/util/testutil/testutil.go
+++ b/util/testutil/testutil.go
@@ -193,6 +193,26 @@ func loadTestSuiteCases(filePath string) (res []testCases, err error) {
 	return res, err
 }
 
+// GetTestCasesByName gets the test cases for a test function by its name.
+func (t *TestData) GetTestCasesByName(caseName string, c *check.C, in interface{}, out interface{}) {
+	casesIdx, ok := t.funcMap[caseName]
+	c.Assert(ok, check.IsTrue, check.Commentf("Must get test %s", caseName))
+	err := json.Unmarshal(*t.input[casesIdx].Cases, in)
+	c.Assert(err, check.IsNil)
+	if !record {
+		err = json.Unmarshal(*t.output[casesIdx].Cases, out)
+		c.Assert(err, check.IsNil)
+	} else {
+		// Init for generate output file.
+		inputLen := reflect.ValueOf(in).Elem().Len()
+		v := reflect.ValueOf(out).Elem()
+		if v.Kind() == reflect.Slice {
+			v.Set(reflect.MakeSlice(v.Type(), inputLen, inputLen))
+		}
+	}
+	t.output[casesIdx].decodedOut = out
+}
+
 // GetTestCases gets the test cases for a test function.
 func (t *TestData) GetTestCases(c *check.C, in interface{}, out interface{}) {
 	// Extract caller's name.