I feel like the solution to this is painfully obviously, but I just can't seem to get it right... Any help would be greatly appreciated.

$\displaystyle f(x)=\int_{3}^{x^3}{t^2}{dt}$

It wants to know $\displaystyle f'(x)$. Wouldn't that just be $\displaystyle x^2$ then? Since the derivative cancels out the integral? What is messing me up is the limits, since I am pretty sure they make it something other than $\displaystyle x^2$.