Let $f : \mathbb{R} \longrightarrow \mathbb{R}$ be twice continuously differentiable. Suppose further that $f''(x) \geq 0$ for every $x \in \mathbb{R}$. Choose the correct statement(s) from below:\\
(A) $f$ is bounded;\\
(B) $f$ is constant;\\
(C) If $f$ is bounded, then it is infinitely differentiable;\\
(D) $\int_0^x f(t)\,\mathrm{d}t$ is infinitely differentiable with respect to $x$.