Calculus #1

Calculus Level 3

$\large F(x) = \int^{x^3}_{x^2} \ln t \ dt$

$F(x)$ is defined as above for $x>0$ . If $F'(2) = a \ln b$ , where $a$ and $b$ are positive integers with $b$ being a prime, find $a+b$ .

Note: $F'(x)$ denotes the first derivative of $F(x)$ with respect to $x$ .