China Mathematical Competition

On a coordinate plane there are two regions, $M$ and $N$: $M$ is confined by $$\{\begin{array}{l}y\ge 0,\\ y\le x,\\ y\le 2-x\end{array}$$ and $N$ is determined by the inequalities $t\le x\le t+1$, $0\le t\le 1$. Then the size of the common area of $M$ and $N$ is given by $f(t)=\underline{}$.