I was facing the same problem and I found the solution 
Android's official Documentation about WebView
Here is my onCreateView() method and here i used two methods to open the urls 
Method 1 is opening url in Browser and 
Method 2 is opening url in your desired WebView.
And I am using Method 2 for my Application and this is my code:
public class MainActivity extends Activity {
   private WebView myWebView;
     @Override
     public View onCreateView(LayoutInflater inflater, ViewGroup container, Bundle savedInstanceState) {
      View rootView = inflater.inflate(R.layout.fragment_webpage_detail, container, false);
      // Show the dummy content as text in a TextView.
      if (mItem != null) {
         /* Method : 1
          This following line is working fine BUT when we click the menu item then it opens the URL in BROWSER not in WebView */
         //((WebView)   rootView.findViewById(R.id.detail_area)).loadUrl(mItem.url);
        // Method : 2
        myWebView = (WebView) rootView.findViewById(R.id.detail_area); // get your WebView form your xml file
        myWebView.setWebViewClient(new WebViewClient()); // set the WebViewClient
        myWebView.loadUrl(mItem.url); // Load your desired url
    }
    return rootView;
}                                                                                               }