JEE Math Practice Question

Let $$f(x)$$ be a non - negative continuous function such that the area bounded by the curve $$y=f(x),$$ $$x$$-axis and the ordinates $$x = {\pi \over 4}$$ and $$x = \beta > {\pi \over 4}$$ is $$\left( {\beta \sin \beta + {\pi \over 4}\cos \beta + \sqrt 2 \beta } \right).$$ Then $$f\left( {{\pi \over 2}} \right)$$ is

1. A.$$\left( {{\pi \over 4} + \sqrt 2 - 1} \right)$$
2. B.$$\left( {{\pi \over 4} - \sqrt 2 + 1} \right)$$
3. C.$$\left( {1 - {\pi \over 4} - \sqrt 2 } \right)$$
4. D.$$\left( {1 - {\pi \over 4} + \sqrt 2 } \right)$$