$f:[0,\infty) \to [0,\infty)$ continuous function such that $\int_0^{\infty} f(x) dx$ is convergent ; is $\{f(n)\}$ bounded?
Prove that $f$ continuous and $\int_a^\infty |f(x)|\;dx$ finite imply $\lim\limits_{ x \to \infty } f(x)=0$