running implementation of behavior

workingSampleTabBar.dart

import 'package:flutter/material.dart';

void main() => runApp(new MyApp());

class MyApp extends StatefulWidget {
  @override
  _MyAppState createState() => new _MyAppState();
}

class _TabBarContainer extends StatelessWidget {
  final TabController tabController;

  _TabBarContainer({
    this.tabController,
  });

  @override
  Widget build(BuildContext context) {
    return Container(
      color: Colors.blue,
      child: Column(
        children: <Widget>[
          TabBar(
            controller: tabController,
            tabs: [
              Tab(text: "Yellow"),
              Tab(text: "Grey"),
            ],
          ),
          Expanded(
            flex: 1,
            child: TabBarView(
              controller: tabController,
              children: <Widget>[
                Container(color: Colors.yellow),
                Container(color: Colors.grey),
              ],
            ),
          )
        ],
      ),
    );
  }
}

class _MyAppState extends State<MyApp> with TickerProviderStateMixin {
  TabController _tabController;
  List<Widget> _widgetList;
  int _selectedIndex = 0;

  @override
  void initState() {
    super.initState();
    _tabController = TabController(length: 2, vsync: this);
    _widgetList = [
      Container(color: Colors.red),
      _TabBarContainer(tabController: _tabController),
      Container(color: Colors.green),
      Container(color: Colors.indigo),
    ];
  }

  @override dispose() {
    _tabController.dispose();
    super.dispose();
  }

  @override
  Widget build(BuildContext context) {
    return MaterialApp(
      home: new Scaffold(
        body: _widgetList.elementAt(_selectedIndex),
        bottomNavigationBar: BottomNavigationBar(
          currentIndex: _selectedIndex,
          onTap: (int index) {
            setState(() {
              _selectedIndex = index;
            });
          },
          type: BottomNavigationBarType.fixed,
          items: <BottomNavigationBarItem>[
            BottomNavigationBarItem(icon: Icon(Icons.add), title: Text("Tab")),
            BottomNavigationBarItem(icon: Icon(Icons.add), title: Text("Tab")),
            BottomNavigationBarItem(icon: Icon(Icons.add), title: Text("Tab")),
            BottomNavigationBarItem(icon: Icon(Icons.add), title: Text("Tab")),
          ],
        ),
      ),
    );
  }
}