Let f be a differentiable function satisfying f(x)=1-2 x+∫_0^x e^(x-t) f(t) dt, x ∈ R and let g (x)=∫_0^x(f( t )+2)^15( t -4)^6( t +12)^17 dt, x ∈ R.…

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