Since every .subscribe() call returns a Disposable interface, it is the easiest way to terminate Subscriptions that are no longer needed; they can be canceled with a reference to the returned object.

In a simplified case, it will look like this:

private Disposable disposable;

@Override
protected void onCreate(Bundle savedInstanceState) {
    super.onCreate(savedInstanceState);
    setContentView(R.layout.activity_mock);

    disposable = Observable.interval(1, TimeUnit.SECONDS)
            .subscribe();
}

@Override
protected void onDestroy() {
    if (disposable != null) {
        disposable.dispose();
    }
    super.onDestroy();
}

Here, on the first line, we've created a field to keep a reference to the Disposable after it gets created:

private Disposable subscribe;

Next, in the onCreate() block, we have the Observable and the Subscription created with this:

disposable = Observable.interval(1, TimeUnit.SECONDS)
        .subscribe();

Also, we assign the Disposable reference.

Now, when the Activity is destroyed, the onDestroy() method will be called and the Subscription will be disposed of (canceled) with the following:

if (subscribe != null) {
    subscribe.dispose();
}

The same can be done with onStart-onStop and onResume-onPause pairs. However, it is important not to mix up pairs (such as onStart-onDestroy) as it will most likely lead to leaks or inconsistent behavior of the application.