Integral Calculus: JEE Main 2024 Mathematics question

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