The value of \[\int_{0}^{{{\sin }^{2}}x}{{{\sin }^{-1}}\sqrt{t}\,dt+\int_{0}^{{{\cos }^{2}}x}{{{\cos }^{-1}}\sqrt{t}\,dt}}\] is [MP PET 2001; Orissa JEE 2005]

• A.                 \[\frac{\pi }{2}\]              
• B.                 1
• C.                 \[\frac{\pi }{4}\]              
• D.                 None of these