Fix index of TabBarView when decrementing (#88878)

Small change to the calculation of the page to move to when flinging on a TabBarView

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

@@ -1440,7 +1440,7 @@ class _TabBarViewState extends State<TabBarView> {
     _warpUnderwayCount += 1;
     if (notification is ScrollUpdateNotification && !_controller!.indexIsChanging) {
       if ((_pageController.page! - _controller!.index).abs() > 1.0) {
-        _controller!.index = _pageController.page!.floor();
+        _controller!.index = _pageController.page!.round();
         _currentIndex =_controller!.index;
       }
       _controller!.offset = (_pageController.page! - _controller!.index).clamp(-1.0, 1.0);

packages/flutter/test/material/tabs_test.dart

@@ -600,6 +600,51 @@ void main() {
     expect(find.text('RIGHT CHILD'), findsNothing);
   });
 
+  // A regression test for https://github.com/flutter/flutter/pull/88878.
+  testWidgets('TabController notifies the index to change when left flinging', (WidgetTester tester) async {
+    final List<String> tabs = <String>['A', 'B', 'C'];
+    late TabController tabController;
+
+    Widget buildTabControllerFrame(BuildContext context, TabController controller) {
+      tabController = controller;
+      return MaterialApp(
+        theme: ThemeData(platform: TargetPlatform.iOS),
+        home: Scaffold(
+          appBar: AppBar(
+            title: const Text('tabs'),
+            bottom: TabBar(
+              controller: controller,
+              tabs: tabs.map<Widget>((String tab) => Tab(text: tab)).toList(),
+            ),
+          ),
+          body: TabBarView(
+            controller: controller,
+            children: const <Widget>[
+              Center(child: Text('CHILD A')),
+              Center(child: Text('CHILD B')),
+              Center(child: Text('CHILD C')),
+            ],
+          ),
+        ),
+      );
+    }
+
+    await tester.pumpWidget(TabControllerFrame(
+      builder: buildTabControllerFrame,
+      length: tabs.length,
+      initialIndex: tabs.indexOf('C'),
+    ));
+    expect(tabController.index, tabs.indexOf('C'));
+
+    tabController.addListener(() {
+      final int indexOfB = tabs.indexOf('B');
+      expect(tabController.index, indexOfB);
+    });
+    final Offset flingStart = tester.getCenter(find.text('CHILD C'));
+    await tester.flingFrom(flingStart, const Offset(600, 0.0), 10000.0);
+    await tester.pumpAndSettle();
+  });
+
   // A regression test for https://github.com/flutter/flutter/issues/7133
   testWidgets('TabBar fling velocity', (WidgetTester tester) async {
     final List<String> tabs = <String>['AAAAAA', 'BBBBBB', 'CCCCCC', 'DDDDDD', 'EEEEEE', 'FFFFFF', 'GGGGGG', 'HHHHHH', 'IIIIII', 'JJJJJJ', 'KKKKKK', 'LLLLLL'];