a problem about minimum value

a problem about minimum value

Calculate
\begin{equation*}\text{min}_{a,b,c}\int^1_{-1}|x^3-a-bx-cx^2|^2dx.\end{equation*}
I want to solve it by the theory in Hilbert space $L^2(-1,1)$,but I don't
know how to start.Can anyone give me a help?