Is there a lower bound for $\int_{B_{r}}f$ when $f$ is a positive function?

Is there a lower bound for $\int_{B_{r}}f$ when $f$ is a positive function?

Let $f$ be a positive Lebesgue integrable function on a ball
$B_{r}\in\mathbb{R}^n$. I'm looking for a positive constant $c$ depending
only on $r$ and $f$ that satisfies $$c\omega_nr^n\leq\int_{B_r}f$$ where
$\omega_n$ is the volume of the $n$-dimensional unit ball.
I'm also wondering if the similar result holds for a nonnegative
integrable function $f$ and a nonnegative constant $c=c(r,f)$. Of course,
$c=0$ satisfies the inequality in the this case but I need a positive
constant $c$ unless $f\equiv 0$ a.e. on $B_r$.