For the function \( f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right)\), where \(x \in\left[0, \frac{\pi}{2}\right]\), con…

For the function \( f(x)=\sin x+3 x-\frac{2}{\pi}\left(x^2+x\right)\), 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,

[JEE Main 2024, 5 Apr (Shift 1)]