Chapter 5.4, Problem 52E

In Problems 43–54, calculate the definite integral, given that

$\begin{array}{ccc}{\displaystyle {\int }_1^{4}xdx=7.5}& {\displaystyle {\int }_1^4{x}^{2}dx=21}& {\displaystyle {\int }_4^5{x}^{2}dx=\frac{61}{3}}\end{array}$

52. ${\displaystyle {\int }_5^5\left(10-7x+x^2\right)}dx$