Pinned down by the derivative bound

Let $f:[-1,3]\to\mathbb{R}$ be a continuous function such that $f$ is differentiable on $(-1,3)$, $|f'(x)|\le\dfrac{3}{2}$, $\forall\,x\in(-1,3)$, $f(-1)=1$ and $f(3)=7$. Then $f(1)$ equals __________