Let $$f: [0, 2] \rightarrow R$$ be a function which is continuous on [0, 2] and is differentiable on (0, 2) with f(0) = 1. Let
$$F(x) = \int_{0}^{x^2} f(\sqrt t) dt $$
for $$x \in [0, 2].$$ If $$F^{'}(x) = f^{'} (x)$$ for all $$x \in (0, 2)$$ then F(2) equals

A

$$e^2 - 1$$

B

$$e^4 - 1$$

C

$$e - 1$$

D

$$e^4$$