Fixed scrollable TabBar flashing (#8741)

packages/flutter/lib/src/material/tab_controller.dart

@@ -99,6 +99,7 @@ class TabController extends ChangeNotifier {
     _index = value;
     if (duration != null) {
       _indexIsChangingCount += 1;
+      notifyListeners(); // Because the value of indexIsChanging may have changed.
       _animationController
         ..animateTo(_index.toDouble(), duration: duration, curve: curve).whenComplete(() {
           _indexIsChangingCount -= 1;

packages/flutter/test/material/tabs_test.dart

@@ -618,7 +618,7 @@ void main() {
     expect(secondColor, equals(Colors.blue[500]));
   });
 
-  testWidgets('TabBar unselectedLabelColor control test', (WidgetTester tester) async {
+  testWidgets('TabBarView page left and right test', (WidgetTester tester) async {
     final TabController controller = new TabController(
       vsync: const TestVSync(),
       length: 2,
@@ -635,29 +635,46 @@ void main() {
 
     expect(controller.index, equals(0));
 
-    final TestGesture gesture = await tester.startGesture(const Point(100.0, 100.0));
-
+    TestGesture gesture = await tester.startGesture(const Point(100.0, 100.0));
     expect(controller.index, equals(0));
 
-    await gesture.moveBy(const Offset(-380.0, 0.0));
-
+    // Drag to the left and right, by less than the TabBarView's width.
+    // The selected index (controller.index) should not change.
+    await gesture.moveBy(const Offset(-100.0, 0.0));
+    await gesture.moveBy(const Offset(100.0, 0.0));
     expect(controller.index, equals(0));
+    expect(find.text('First'), findsOneWidget);
+    expect(find.text('Second'), findsNothing);
 
-    await gesture.moveBy(const Offset(-40.0, 0.0));
-
+    // Drag more than the TabBarView's width to the right. This forces
+    // the selected index to change to 1.
+    await gesture.moveBy(const Offset(-500.0, 0.0));
+    await gesture.up();
+    await tester.pump(); // start the scroll animation
+    await tester.pump(const Duration(seconds: 1)); // finish the scroll animation
     expect(controller.index, equals(1));
+    expect(find.text('First'), findsNothing);
+    expect(find.text('Second'), findsOneWidget);
 
-    await gesture.moveBy(const Offset(-40.0, 0.0));
-    await tester.pump();
-
+    gesture = await tester.startGesture(const Point(100.0, 100.0));
     expect(controller.index, equals(1));
 
-    await gesture.up();
-    await tester.pumpUntilNoTransientCallbacks();
+    // Drag to the left and right, by less than the TabBarView's width.
+    // The selected index (controller.index) should not change.
+    await gesture.moveBy(const Offset(-100.0, 0.0));
+    await gesture.moveBy(const Offset(100.0, 0.0));
     expect(controller.index, equals(1));
-
     expect(find.text('First'), findsNothing);
     expect(find.text('Second'), findsOneWidget);
-  });
 
+    // Drag more than the TabBarView's width to the left. This forces
+    // the selected index to change back to 0.
+    await gesture.moveBy(const Offset(500.0, 0.0));
+    await gesture.up();
+    await tester.pump(); // start the scroll animation
+    await tester.pump(const Duration(seconds: 1)); // finish the scroll animation
+    expect(controller.index, equals(0));
+    expect(find.text('First'), findsOneWidget);
+    expect(find.text('Second'), findsNothing);
+  });
 }