Final answer:
The medulla oblongata is the part of the brainstem that controls the heartbeat and breathing, which are vital autonomic functions. Therefore, the correct option is 2.
Step-by-step explanation:
The brainstem is the oldest and innermost region of the brain. The part of the brainstem that controls heartbeat and breathing is the medulla oblongata. It lies directly under the cerebrum and is part of the brain stem, which includes the midbrain, pons, and medulla oblongata. This region of the brain controls vital autonomic functions, such as heart rate, breathing, and blood pressure, among others. The medulla oblongata plays a crucial role in maintaining these life-sustaining processes.