Prove that if $f(x)$ is a polynomial of finite order with integer coefficients and $n$ is an integer, then $f(n)$ is an integer.

Question

Prove that if $f(x)$ is a polynomial of finite order with integer coefficients and $n$ is an integer, then $f(n)$ is an integer.

I'm not to sure where a good logical starting point for this question would be. Could someone please help me start the question off.

Thanks