Final answer:
The autonomic nervous system, which controls involuntary functions of the internal organs and glands, has a sympathetic division that arouses the body and a parasympathetic division that calms it.
Step-by-step explanation:
The part of the peripheral nervous system that controls the glands and muscles of internal organs and has divisions that either arouse or calm the body is known as the autonomic nervous system (ANS). The sympathetic division of the ANS prepares the body for stress-related activities, a response often referred to as 'fight-or-flight.' In contrast, the parasympathetic division helps return the body to a state of rest, maintaining daily operations. These two divisions work in opposition to each other to keep the body in a stable condition called homeostasis.