Let $f : \mathbb{R} \longrightarrow \mathbb{R}$ be such that $\int_{-\infty}^{\infty}|f(x)|\,\mathrm{d}x < \infty$. Define $F : \mathbb{R} \longrightarrow \mathbb{R}$ by $F(x) = \int_{-\infty}^{x} f(t)\,\mathrm{d}t$. Choose the correct statement(s):\\
(A) $f$ is continuous;\\
(B) $F$ is continuous;\\
(C) $F$ is uniformly continuous;\\
(D) There exists a positive real number $M$ such that $|f(x)| < M$ for all $x \in \mathbb{R}$.