Which term names a production that integrates music, dance, sets, and costumes to enhance the
telling of a story?

An opera is the correct answer.

Explanation:

An opera is an extended dramatic composition, characterized because there is music in all of its parts; sometimes there are lyrics and sometimes it is just the musical accompaniment; it sometimes includes a ballet, too. All this elements are put together to create a bigger impact on the audience and to enhance the telling of a story.