Graph of a function whose derivative is periodic

Define $F(x)=\displaystyle \int_c^x f(t) \,dt$ where $c$ is some constant and the period of a continuous function $f(x)$ is $p$ .

For all $k$ , the following equation $F(x)=k$ has $n$ distinct real roots.

When $n=3$ , $F(x)$ has at least $m$ different points whose value is a global maximum/minimum, in some closed interval whose length is $p$ .

Find $m$ .