If \(f\left(a+b-x\right)=f\left(x\right)\) then \(\int_{a}^{b}xf\left(x\right)dx\) is equal to

\(\frac{a+b}{2}\int_{a}^{b}f\left(b-x\right)dx\) \(\frac{a+b}{2}\int_{a}^{b}f\left(b+x\right)dx\) \(\frac{b-a}{2}\int_{a}^{b}f\left(x\right)dx\) \(\frac{a+b}{2}\int_{a}^{b}f\left(a+b-x\right)dx\)

\(\frac{a+b}{2}\int_{a}^{b}f\left(a+b-x\right)dx\)

Use \(\int_{a}^{b}f\left(x\right)dx=\int_{a}^{b}f\left(a+b-x\right)dx\)