add UIViewController in subview

You should use Child containment concept, here MainViewController is a parent view controller and you want to add child view controller view as a subview on Main View Controller.

Adding and Removing a Child

//call displayContentController to add SampleViewCOntroller view to mainViewcontroller
 [self displayContentController:sampleVCObject];

// write this method in MainViewController
- (void) displayContentController: (UIViewController*) content;
{
   [self addChildViewController:content];                 // 1
   content.view.bounds = testView.bounds;                 //2
   [testView addSubview:content.view];
   [content didMoveToParentViewController:self];          // 3
}

Here’s what the code does:

It calls the container’s addChildViewController: method to add the child. Calling the addChildViewController: method also calls the child’s willMoveToParentViewController: method automatically. It accesses the child’s view property to retrieve the view and adds it to its own view hierarchy. The container sets the child’s size and position before adding the view; containers always choose where the child’s content appears. Although this example does this by explicitly setting the frame, you could also use layout constraints to determine the view’s position. It explicitly calls the child’s didMoveToParentViewController: method to signal that the operation is complete.

//you can also write this method in MainViewController to remove the child VC you added before.
- (void) hideContentController: (UIViewController*) content
{
   [content willMoveToParentViewController:nil];  // 1
   [content.view removeFromSuperview];            // 2
   [content removeFromParentViewController];      // 3
}

For more details, please refer to apple doc: https://developer.apple.com/library/content/featuredarticles/ViewControllerPGforiPhoneOS/ImplementingaContainerViewController.html

Configuring a Container in Interface Builder, for those who don't want to write code.

To create a parent-child container relationship at design time, add a container view object to your storyboard scene, as shown in Figure 5-3. A container view object is a placeholder object that represents the contents of a child view controller. Use that view to size and position the child’s root view in relation to the other views in the container.

When you load a view controller with one or more container views, Interface Builder also loads the child view controllers associated with those views. The children must be instantiated at the same time as the parent so that the appropriate parent-child relationships can be created.

You can do this simply by using StoryBoards

• Open storyboards and select the view controller in which your Blue view is present, open Utilities search for ContainerView and drag it into your blue view, this will automatically adds an view controller that acts as child view for your view. You can resize your container view in size inspector.