(3) In the coordinate plane, there are two regions $M$ and $N$. $M$ is defined by 
\[
\left\{\begin{array}{l}
y \geqslant 0, \\
y \leqslant x, \\
y \leqslant 2-x,
\end{array} \quad N\right.
\]
is a region that varies with $t$, determined by the inequality $t \leqslant x \leqslant t+1$, where the range of $t$ is $0 \leqslant t \leqslant 1$. The common area of $M$ and $N$ is a function $f(t)=$ $\qquad$
(3) $-t^{2}+t+\frac{1}{2}$ Hint: From the problem, we know
$$
\begin{aligned}
f(t) & =S_{\text {shadow part area }} \\
& =S_{\triangle A O B}-S_{\triangle O C D}-S_{\triangle B E F} \\
& =1-\frac{1}{2} t^{2}-\frac{1}{2}(1-t)^{2} \\
& =-t^{2}+t+\frac{1}{2} .
\end{aligned}
$$