# The additive function is bounded

Hi,
If I have an additive function which is $f(x+y)=f(x)+f(y)$,
the question is
how can we prove that if this function has a limit at each real number then there is a number a greater than zero and M greater than zero
such that
$|f(x)|\leq M$, for all $x\in[-a,a]$,