The verbal phrase is Unlimited.
I'm pretty sure the answer is B) The cleaning lady. Cause she discovered he was dead and cleaned his room out for him.
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.
B sounds like the logical answer (I might be wrong though )