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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


( A ) 41
( B ) 21
( C ) 42
( D ) $\sqrt{41}$

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