Final answer:
The brain stem and cerebellum are the main parts of the brain responsible for processing balance and movement information from the mechanoreceptors in the inner ear's vestibule.
Step-by-step explanation:
The part of the brain that integrates information from mechanoreceptors in the inner ear primarily includes the brain stem and the cerebellum. Mechanoreceptors like the hair cells in the utricle, saccule, and semicircular canals of the vestibule detect head position and movement. These signals are transmitted through bipolar neurons to various parts of the brain, including the brain stem's cochlear nucleus, and then ascend to other regions, such as the pons, thalamus, cerebellum, and somatosensory cortex. These pathways are crucial for balance, coordination, and perceiving motion, and they even influence eye movements to maintain visual stability.