Chapter 8.8, Problem 64E

To determine

To show that $S_2$ also gives the exact value for ${\displaystyle \underset{a}{\overset{b}{\int }}{x}^{3}dx}$ and conclude that $S_N$is exact for all cubic polynomials and show by counter-example that $S_2$is not exact for integrals of $x^4$