Integral with function calculation

Question

I would like some help in calculating the following integral

$$ y(t)= \int_{-\infty}^{\infty} u(τ)u(t-τ+5) dτ $$

where $$u(t) = \begin{cases} 1 & \,, t>0 \\ \frac12 & \,, t=0 \\ 0 & \,, t<0 \end{cases} $$

Answer 1

Hint:

The integrand is $1$ on some finite interval and $0$ elsewhere (also $\frac12$ at endpoints but this does not matter as these points have null measure).

Find the width of the interval.