This is a homework exercise, and ''Thomas early trascendentals'' book vol.4 says in property that :
Def: To integrate an absolute value function, we have to look for specific cases when ; $ v(t)\leqslant 0 ; v(t)\geqslant 0$
$v(t)$ in this case is,$ \frac{x-2}{x+5} for\quad I\in[0,4] $
Furthermore, in my following steps I concluded that i must separate the integrals in sum :
$\int_0^2\left(\frac{-(x-2)}{x+5}\right) dx + \int_2^4\left(\frac{x-2}{x+5}\right)dx $ I am right with that intervals?
And that is
$\int_0^4\lvert (\frac{x-2}{x+5})\rvert dx $