Chapter 1.2, Problem 102E

In the following exercises, given that ${\displaystyle {\int }_0^{1}xdx=\frac{1}{2}},{\displaystyle {\int }_0^1{x}^{2}dx=\frac{1}{3}}$ , and ${\displaystyle {\int }_0^1{x}^{3}dx=\frac{1}{4}}$ compute the integrals.

102. ${\displaystyle {\int }_0^1\left(6x-\frac{4}{3}{x}^2\right)dx}$