Evaluate the integral using any appropriate algebraic method or trigonometric identity.

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{10{}^3-24{}^2+19}{5-7}d$

${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}\frac{10{}^3-24{}^2+19}{5-7}d=$

$$

$($Type an exact answer. Use parentheses to clearly denote the argument of each function.$)$