# Minima Problema

Calculus Level 5

$$p$$ and $$q$$ are constants for which

$f(p,q)=\int_0^\pi \left(\sin x-(px^2+qx)\right)^2\;dx$

has a minimum value. If

$p+q=\frac{a}{\pi^2}+\frac{b}{\pi^3}+\frac{c}{\pi^4}+\frac{d}{\pi^5},$

then what is the value of $$a+b+c+d$$?

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