Answer:
Yes, because it is the moral of a story or s message the author is trying to tell you. So it is important.
Infinitives in the English language are relatives easy to spot. You just have to locate the word TO followed by a verb.
Here, the infinitive is to eat.
There is another TO in the sentence (to music), however, the word music is not a verb, which means that <em>to music </em>is not an infinitive.
Hungry is the best answer
Identify the adjective clause and the word it modifies.
The tree whose branches had died had to be cut down.
is the question