For each part below, what is $F^\prime(x)$?

1. $F(x)=\int_5^{x^2}\cos(\ln(t))dt$

   Hint (a):

   The derivative of an integral is the original function, but this integral has bounds.

   Answer (a):

   $F^\prime(x) = 2\cos(\ln(x^2) − 0$

2. $F(x)=\int_{\sin(x)}^{\cos(x)}\frac{1}{t^2+1}dt$

   Hint (b):

   Notice the upper bound AND the lower bound.