Chapter 5.2, Problem 12E

To determine

Find $c_1, c_2$ and $c_3$ such that the rule $\underset{0}{\overset{1}{{\displaystyle \int }}}f\left(x\right) dx\approx c_{1}f\left(0\right)+c_{2}f\left(0.5\right)+c_{3}f\left(1\right)$ has degree of precision greater than one.