Solve question 8:

8. The range of function $\mathrm{f}\left(\mathrm{x}\right)={\sin }^{-1}\left[{\mathrm{x}}^2+\frac{1}{2}\right]+{\cos }^{-1}\left[{\mathrm{x}}^2+\frac{1}{2}\right]$, where [.] is the greatest integer function is:- 
$\left(A\right) \left\{\frac{\mathrm{\pi }}{2},\mathrm{\pi }\right\} \left(B\right) \left\{0,\frac{-1}{2}\right\} \left(C\right) \left\{\mathrm{\pi }\right\} \left(D\right) \left\{0, \frac{\mathrm{\pi }}{2}\right\}$