Learn Russian: Большинство местных студентов изучает искусство. - The majority of local students study art.

It is in the genitive plural form to match студентов (students). We use the genitive case here because it follows the word Большинство (the majority). Just like English uses the word 'of' in 'the majority of', Russian uses the genitive case to show this connection.

Why is the verb изучает singular if the sentence is about plural students?

The grammatical subject of the sentence is actually Большинство (majority), which is a singular neuter noun. Because of this, the verb must also be singular (изучает instead of the plural изучают).

Why doesn't the word искусство (art) change its ending, since it is the direct object?

It is actually in the accusative case because it is the direct object of the verb изучает. However, because искусство is an inanimate neuter noun, its accusative form looks exactly the same as its dictionary (nominative) form.

Could I use учит instead of изучает for the word 'study'?

In this context, изучает is the best choice. The verb изучать is used when studying a specific academic subject or discipline in depth, like art, history, or physics. Учить is more often used for memorizing things (like vocabulary) or learning a basic skill.