Answer
Three principal divisions of the brain are the cerebrum, cerebellum, and the brainstem.
The brainstem is defined as the rest of the brain except the cerebrum and cerebellum (this is the definition used in this book). The brainstem includes the diencephalon, midbrain, pons, and medulla oblongata. Some people exclude the diencephalon from the brainstem.
Work Step by Step
The cerebrum is in charge of higher level thinking. The cerebellum is in charge of balance and motor coordination. The brainstem is in charge of functions related to living (like breathing, CV, hunger/thirst, etc).
Some people include the diencephalon in the brainstem because they define the brainstem as everything but the cerebrum and cerebellum. Those that exclude the diencephalon from the brainstem argue that since the diencephalon arises from the prosencephalon (forebrain) in fetal development, it should be classified with the cerebrum as part of the forebrain.
This book says the diencephalon belongs in the brainstem.