Let $$p(x)$$ be a function defined on $$R$$ such that $$p'(x) = p'(1 - x)$$, for all $$x \in [0, 1]$$, $$p(0) = 1$$ and $$p(1) = 41$$. Then $$\int_0^1 p(x) \, dx$$ equals

A

$$21$$

B

$$41$$

C

$$42$$

D

$$\sqrt{41}$$