Question:

Let $f$ be a differentiable function satisfying $f(x)=1-2x+\displaystyle\int_0^x e^{(x-t)}f(t)\,\mathrm{d}t$, $x\in\mathbf{R}$ and let $g(x)=\displaystyle\int_0^x (f(t)+2)^{15}(t-4)^6(t+12)^{17}\,\mathrm{d}t$, $x\in\mathbf{R}$. If $p$ and $q$ are respectively the points of local minima and local maxima of $g$, then the value of $|p+q|$ is equal to _____