# Second derivative

$F'(x) = \frac{d}{dx} \int_1^x f(t) dt = f(x)$ by the fundamental theorem of calculus. So $F''(2) = f'(2)$.
You can find $f'(t)$ using the fundamental theorem of calculus as well. You should get $f'(t) = 4t^3 \frac{\sqrt{5+t^{16}}}{t^4}$ (there's a chain rule application in there as well).