Integral Calculus: JEE Main 2005 Mathematics 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