area of the region bounded by the curve \( y=\frac{16-x^{2}}{4} \) and \( y=\sec ^{-1}\left[-\si...

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area of the region bounded by the curve \( y=\frac{16-x^{2}}{4} \) and \( y=\sec ^{-1}\left[-\sin ^{2} x\right] \) (where [] denotes the greatest integer function)
(A) \( \frac{1}{3}(4-\pi)^{3 / 2} \)
(B) \( 8(4-1)^{3 / 2} \)
(C) \( \frac{8}{3}(4-\pi)^{3 / 2} \)
(D) \( \frac{8}{3}(4-x)^{1 / 2} \)
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