A calculus problem by avi solanki

Let $\displaystyle f(x) = e^{-1/x^2} + \int_0^{\pi x/2} \sqrt{1 + \sin t} \, dt\quad \forall x \in (0, \infty)$ , then which of the following statements is true?

(A): $f'$ exists and is continuous $\forall x \in (0,\infty)$ .
(B): $f''$ exists $\forall x\in (0,\infty)$ .
(C): $f'$ is bounded.
(D): There exists $\alpha > 0$ such that $| f(x) | > | f'(x) | \; \forall x \in (\alpha ,\infty)$ .