TITLE: Evaluating definite integral of $p(x)$
QUESTION [9 upvotes]: Let $p(x)$ be fifth degree polynomial such that $p(x)+1$ is divisible by $(x-1)^3$ and $p(x)-1 $is divisible by $(x+1)^3 $. Then find the value of the definite integral $$\int _{-10}^{10}p(x)dx$$ 

Attempt: 
$p(x)-1 = (x+1)^3 Q(x)$
$p(x)+1 = (x-1)^3 H(x)$
Where $Q(x)$ and $H(x)$ are unknown quadratics. 
But there's not sufficient information to find $Q$ and $H$ thats why I am unable to proceed. 
Please provide only a guiding hint, I want to solve it myself.

REPLY [5 votes]: Thanks to @KeyFlex answer, if both $(x-1)^2$ and $(x+1)^2$ divide $p^{\prime}(x)$, then since $p'$ is degree $4$ so
$$p'(x)=k(x^2-1)^2$$
for a real $k$, hence $p'$ is even and then $p$ is odd which concludes  $$\int_{-10}^{10}p(x)dx=0$$