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Let $f(x)$ be a differentiable function defined on $[0, 2]$ such that $f’(x) = f’(2 - x)$ for all $x \in (0, 2)$, $f(0) = 1$ and $f(2) = e^2$. Then the value of $\int_0^2 f(x),dx$ is:
(1) $1 + e^2$
(2) $1 - e^2$
(3) $2(1 - e^2)$
(4) $2(1 + e^2)$
BETA
