JEE Math Practice Question

For the function $$f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right), \text { where } x \in\left[0, \frac{\pi}{2}\right],$$ consider the following two statements : (I) $$f$$ is increasing in $$\left(0, \frac{\pi}{2}\right)$$. (II) $$f^{\prime}$$ is decreasing in $$\left(0, \frac{\pi}{2}\right)$$. Between the above two statements,

1. A.only (I) is true.
2. B.both (I) and (II) are true.
3. C.only (II) is true.
4. D.neither (I) nor (II) is true.