5. Let two regions on the Cartesian plane be $M=\left\{(x, y) \in \mathbf{R}^{2} \mid 0 \leqslant y \leqslant \min (2 x, 3-x)\right\}, N=$ $\left\{(x, y) \in \mathbf{R}^{2} \mid t \leqslant x \leqslant t+2\right\}$, and let the area of the intersection of $M$ and $N$ be $f(t)$. When $0 \leqslant t \leqslant 1$, the expression for $f(t)$ is $\qquad$.
Given the points $A(t, 2t)$ and $D(t+2, 1-t)$, we have
$$
\begin{array}{l}
f(t)=S_{\triangle O E F}-S_{\triangle O A B}-S_{\triangle D C F} \\
=3-t^{2}-\frac{1}{2}(1-t)^{2}=-\frac{3}{2} t^{2}+t+\frac{5}{2}
\end{array}
$$