for example I have somethink like that,
$ \begin{align*} f(x) &= \begin{cases} \frac{1}{3}x - \frac{2}{3} &\text{where }2 < x \leq 4, \\ \frac{-2}{3}x + \frac{10}{3} &\text{where }4 < x \leq 5. \end{cases}\\ g(x) &= \frac{-1}{2}x + \frac{3}{2} \qquad\qquad\text{where }1 \leq x \leq 3. \\ \end{align*}$
and I would like to know how the intervals of integration look, when $f(x)$ has 2 intervals.