How to compute a simple convolution

Question

$$ q(t)=\begin{cases} 0& t<0\\\\ 1-t& 0<t<1\\\\ 0& t>1 \end{cases}$$

How do I compute the $ h(t) = \int_{-\infty}^{\infty} q(t+\tau ) d \tau $

I know this suppose to be basic but I get very confused on how to do it.

Answer 1

Fix $t$. Then, $$q(t+\tau)=\begin{cases}0&t+\tau<0\\1-(t+\tau)&0<t+\tau<1\\0&t+\tau>1\end{cases}.$$

Therefore, $$\int_{-\infty }^\infty q(t+\tau)\,\mathrm d \tau=\int_{-t}^{1-t}1-(t+\tau)\,\mathrm d \tau=...$$