If f(x) = integrate t^2 from x to x^2, then

Question

f'(x)=
f'(-1)=

Please help! I have no idea how to approach this.

Answer 1

f'(x) = (x^2)^2 (2x) - x^2 (1)
= 2x^5-x^2

Google

differentiation under the integral

for several explanations. Wikipedia has a good article.

This is really just the chain rule in reverse.