diff --git a/statistics/ddl_test.go b/statistics/ddl_test.go
index a0f70babc5..4b4eb456b8 100644
--- a/statistics/ddl_test.go
+++ b/statistics/ddl_test.go
@@ -84,7 +84,7 @@ func (s *testStatsCacheSuite) TestDDLTable(c *C) {
 	statsTbl = h.GetTableStats(tableInfo.ID)
 	c.Assert(statsTbl.Pseudo, IsTrue)
 
-	testKit.MustExec("create table t1 (c1 int, c2 int)")
+	testKit.MustExec("create table t1 (c1 int, c2 int, index idx(c1))")
 	is = do.InfoSchema()
 	tbl, err = is.TableByName(model.NewCIStr("test"), model.NewCIStr("t1"))
 	c.Assert(err, IsNil)
diff --git a/statistics/statistics_test.go b/statistics/statistics_test.go
index b8940bfdd3..ea7561d978 100644
--- a/statistics/statistics_test.go
+++ b/statistics/statistics_test.go
@@ -14,6 +14,7 @@
 package statistics
 
 import (
+	"math"
 	"testing"
 
 	. "github.com/pingcap/check"
@@ -180,6 +181,7 @@ func (s *testStatisticsSuite) TestBuild(c *C) {
 	c.Check(err, IsNil)
 	c.Check(int(count), Equals, 0)
 
+	s.pk.(*recordSet).cursor = 0
 	tblCount, col, err = BuildPK(ctx, bucketCount, 4, ast.RecordSet(s.pk))
 	c.Check(err, IsNil)
 	c.Check(int(tblCount), Equals, 100000)
@@ -266,6 +268,10 @@ func (s *testStatisticsSuite) TestColumnRange(c *C) {
 	count, err = tbl.GetRowCountByColumnRanges(sc, 0, ran)
 	c.Assert(err, IsNil)
 	c.Assert(int(count), Equals, 2500)
+	ran[0].Low = ran[0].High
+	count, err = tbl.GetRowCountByColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 100)
 
 	tbl.Columns[0] = col
 	ran[0].Low = types.Datum{}
@@ -285,4 +291,68 @@ func (s *testStatisticsSuite) TestColumnRange(c *C) {
 	count, err = tbl.GetRowCountByColumnRanges(sc, 0, ran)
 	c.Assert(err, IsNil)
 	c.Assert(int(count), Equals, 9965)
+	ran[0].Low = ran[0].High
+	count, err = tbl.GetRowCountByColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 1)
+}
+
+func (s *testStatisticsSuite) TestIntColumnRanges(c *C) {
+	bucketCount := int64(256)
+	ctx := mock.NewContext()
+	sc := ctx.GetSessionVars().StmtCtx
+
+	s.pk.(*recordSet).cursor = 0
+	rowCount, hg, err := build4SortedColumn(ctx, bucketCount, 0, s.pk, true)
+	c.Check(err, IsNil)
+	c.Check(rowCount, Equals, int64(100000))
+	col := &Column{Histogram: *hg}
+	tbl := &Table{
+		Count:   int64(col.totalRowCount()),
+		Columns: make(map[int64]*Column),
+	}
+	ran := []types.IntColumnRange{{
+		LowVal:  math.MinInt64,
+		HighVal: math.MaxInt64,
+	}}
+	count, err := tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 100000)
+	ran[0].LowVal = 1000
+	ran[0].HighVal = 2000
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 1000)
+	ran[0].LowVal = 1001
+	ran[0].HighVal = 1999
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 998)
+	ran[0].LowVal = 1000
+	ran[0].HighVal = 1000
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 100)
+
+	tbl.Columns[0] = col
+	ran[0].LowVal = math.MinInt64
+	ran[0].HighVal = math.MaxInt64
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 100000)
+	ran[0].LowVal = 1000
+	ran[0].HighVal = 2000
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 1000)
+	ran[0].LowVal = 1001
+	ran[0].HighVal = 1999
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 998)
+	ran[0].LowVal = 1000
+	ran[0].HighVal = 1000
+	count, err = tbl.GetRowCountByIntColumnRanges(sc, 0, ran)
+	c.Assert(err, IsNil)
+	c.Assert(int(count), Equals, 1)
 }