JEE Math Practice Question

Let $$g:(0,\infty ) \to R$$ be a differentiable function such that $$\int {\left( {{{x(\cos x - \sin x)} \over {{e^x} + 1}} + {{g(x)\left( {{e^x} + 1 - x{e^x}} \right)} \over {{{({e^x} + 1)}^2}}}} \right)dx = {{x\,g(x)} \over {{e^x} + 1}} + c} $$, for all x > 0, where c is an arbitrary constant. Then :

1. A.g is decreasing in $$\left( {0,{\pi \over 4}} \right)$$
2. B.g' is increasing in $$\left( {0,{\pi \over 4}} \right)$$
3. C.g + g' is increasing in $$\left( {0,{\pi \over 2}} \right)$$
4. D.g $$-$$ g' is increasing in $$\left( {0,{\pi \over 2}} \right)$$