JEE Math Practice Question

Let the slope of the tangent to a curve y = f(x) at (x, y) be given by 2 $$\tan x(\cos x - y)$$. If the curve passes through the point $$\left( {{\pi \over 4},0} \right)$$, then the value of $$\int\limits_0^{\pi /2} {y\,dx} $$ is equal to :

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