# 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 \begin{align*} \int_0 ^1p(x) \; dx\end{align*} equals
( D ) $\sqrt{41}$