If $f(x) = A \sin \bigg( \large\frac{\pi x}{2}\bigg)$$+B;f'\bigg(\large\frac{1}{2}\bigg)=$$\sqrt 2$ and $\int \limits_0^1 f(x)dx= \large\frac{2A}{\pi}$

Question

$\begin{array}{1 1} \frac{\pi}{2}\;and\;\large\frac{\pi}{2} \\ \frac{2}{\pi}\;and\;\frac{3}{\pi} \\ 0\;and\;\frac{-4}{\pi} \\ \frac{4}{\pi}\;and\;0 \end{array}$