Let f(x)=|(x-1)(x^2-2 x-3)|+x-3, x ∈ R. If m and M are respectively the number of points of local minimum and local maximum of f in the interval…

Let $\displaystyle f(x)=\left|(x-1)\left(x^2-2 x-3\right)\right|+x-3, x \in \mathbb{R}$. If $\displaystyle m$ and $\displaystyle M$ are respectively the number of points of local minimum and local maximum of $\displaystyle f$ in the interval $\displaystyle (0,4)$, then $\displaystyle m+M$ is equal to \_\_\_\_.