How to add button in ActionBar(Android)?

I want to add a Button to the Action Bar to the right hand side of Example as in this screen shot:

I get actionBar in onCreate method as:

ActionBar actionBar = getActionBar();
actionBar.setDisplayHomeAsUpEnabled(true);

and back button(onOptionsItemSelected method) as below:

public boolean onOptionsItemSelected(MenuItem item){
    Intent myIntent = new Intent(getApplicationContext(),MainActivity.class);
    startActivityForResult(myIntent, 0);
    return true;
}

How can I add button?

you have to create an entry inside res/menu,override onCreateOptionsMenu and inflate it

@Override
public boolean onCreateOptionsMenu(Menu menu) {
    MenuInflater inflater = getMenuInflater();
    inflater.inflate(R.menu.yourentry, menu);
    return true;
}

an entry for the menu could be:

<menu xmlns:android="http://schemas.android.com/apk/res/android" >
    <item
        android:id="@+id/action_cart"
        android:icon="@drawable/cart"
        android:orderInCategory="100"
        android:showAsAction="always"/> 
</menu>

An activity populates the ActionBar in its onCreateOptionsMenu() method.

Instead of using setcustomview(), just override onCreateOptionsMenu like this:

@Override    
public boolean onCreateOptionsMenu(Menu menu) {
  MenuInflater inflater = getMenuInflater();
  inflater.inflate(R.menu.mainmenu, menu);
  return true;
}

If an actions in the ActionBar is selected, the onOptionsItemSelected() method is called. It receives the selected action as parameter. Based on this information you code can decide what to do for example:

@Override
public boolean onOptionsItemSelected(MenuItem item) {
  switch (item.getItemId()) {
    case R.id.menuitem1:
      Toast.makeText(this, "Menu Item 1 selected", Toast.LENGTH_SHORT).show();
      break;
    case R.id.menuitem2:
      Toast.makeText(this, "Menu item 2 selected", Toast.LENGTH_SHORT).show();
      break;
  }
  return true;
}