Definite Integration

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 _________.