problems $1-12,$ calculate the definite integral, given that

${\displaystyle \underset{1}{\overset{4}{}}}xdx=\frac{15}{2},{\displaystyle \underset{1}{\overset{4}{}}}{x}^{2}dx=21,{\displaystyle \underset{4}{\overset{5}{}}}{x}^{2}dx=\frac{61}{3}$

${\displaystyle \underset{1}{\overset{4}{}}}-7xdx$

${\displaystyle \underset{1}{\overset{4}{}}}8x^{2}dx$

${\displaystyle \underset{4}{\overset{1}{}}}(-3x-7x^2)dx$

${\displaystyle \underset{1}{\overset{4}{}}}(7x-10x^2)dx$

${\displaystyle \underset{1}{\overset{4}{}}}(3x^2-9x)dx$

${\displaystyle \underset{4}{\overset{1}{}}}(5x^2-2x)dx$