The graph of f(x)= integral from 0 to x (15(t^2) - 2(t^3) + 24)dt is concave up on (a,b). Find b-a.

Okay so I know from the curve sketching lesson in AB calculus that to find concavity you take the second derivative and then set that to 0. Do I take the integral and then take the first derivative, and then the second?