\int_0^1 {\left( {x - \frac{1}
{2}} \right)^2 \sin \left( {\pi x} \right)dx} = \int_0^1 {x^2 \sin \left( {\pi x} \right)dx} - \int_0^1 {x\sin \left( {\pi x} \right)dx} + \frac{1}
{4}\int_0^1 {\sin \left( {\pi x} \right)dx}