$x(t)=\begin{cases}1 & 0<t<2\\0 & \text{else}\end{cases}$ and $h(t)=\begin{cases}1-t & 0<t<1\\0 & \text{else}\end{cases}$ Calculate $y(t)= x(t)*h(t)$

Question

Let

$$x(t)=\begin{cases}1 & 0<t<2\\0 & \text{else}\end{cases}$$

and

$$h(t)=\begin{cases}1-t & 0<t<1\\0 & \text{else}\end{cases}$$

Calculate $y(t)= x(t)*h(t)$. The farthest I reached was doing the graphs and

\begin{align*} x(t) & =n[t-1]\\ y(t) & =n[1-t][t/2] \end{align*}

Could you guys lend a hand?