what if x appears inside the integral?

find f'(x) for f(x) = integral from a to b of g(x,t) dt

and then

use this result to evaluate I= integral from 0 to 1 of (t^2)*(e^(-t)) dt

and they give you a hint which makes no sense to me

Hint: Compute integral from 0 to 1 of e^(-st) dt

where s is a parameter

How is I related to this integral?