2017 September Korea CSAT Mock test #21 for science&engineering students

For some function $f(x)$ and $g(x)$ which is differentiable in all positive real numbers, following conditions (A), (B), and (C) are true.

(A) $(\frac{f(x)}{x})'$ = $x^2 e^{-x^2}$

(B) $g(x) =\frac{4}{e^4} \int_{1}^{x} e^{t^2} f(t) dt$

(C) $f(1) = \frac{1}{e}$

calculate the value of $f(2) - g(2)$