Let S=(-1, ∞) and f: S → R be defined as f(x)=∫_-1^x(e^t-1)^11(2 t-1)^5(t-2)^7(t-3)^12(2 t-10)^61 d t, Let p = Sum of squares of the values of x,…

Let $\displaystyle S=(-1, \infty)$ and $\displaystyle f: S \rightarrow \mathbb{R}$ be defined as $$f(x)=\int_{-1}^x\left(e^t-1\right)^{11}(2 t-1)^5(t-2)^7(t-3)^{12}(2 t-10)^{61} d t, $$ Let $\displaystyle \mathrm{p}=$ Sum of squares of the values of $\displaystyle x$, where $\displaystyle f(x)$ attains local maxima on $\displaystyle S$, and $\displaystyle \mathrm{q}=$ Sum of the values of x , where $\displaystyle f(x)$ attains local minima on $\displaystyle S$. Then, the value of $\displaystyle p^2+2 q$ is $\displaystyle \_\_\_\_$