Complex sentence: This is the only movement from the Carnival of the Animals that the composer would allow to be played in public during his lifetime as he thought the remaining movements were too frivolous and would damage his reputation as a serious composer.
Split into simpler sentences: This is the only movement from "The Carnival of the Animals" that the composer allowed to be played in public during his lifetime. He thought the remaining movements were too frivolous and would damage his reputation as a serious composer.