\(p\) 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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