Chapter 4.6, Problem 11ES

To determine

The constants $a,b,c\text{ and }d$ that will produce a quadrature formula ${\displaystyle \underset{-1}{\overset{1}{\int }}f\left(x\right)dx}=af\left(-1\right)+bf\left(1\right)+c{f}^{\prime }\left(-1\right)+d{f}^{\prime }\left(1\right)$ that has degree of precision three.