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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.

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maybe you want to give the two functions different names (like $f_1$ and $f_2$ or $f$ and $g$)? –  Fabian Jan 12 '12 at 18:00
    
Maybe you want to write down what you mean by convolution. More specifically, if $h = f*g$, how would you go about computing the value of $h(0)$? No, not how you would go about computing $h(x)$, just $h(0)$ which is a number. –  Dilip Sarwate Jan 12 '12 at 18:35
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