Given \( f(x)=\left|\begin{array}{ccc}0 & x^{2}-\sin x & \cos x-2 \\ \sin x-x^{2} & 0 & 1-2 x \\...
Given \( f(x)=\left|\begin{array}{ccc}0 & x^{2}-\sin x & \cos x-2 \\ \sin x-x^{2} & 0 & 1-2 x \\ 2-\cos x & 2 x-1 & 0\end{array}\right| \), \( \int f(x) d x \) is equal to
(A) \( \frac{x^{3}}{3}-x^{2} \sin x+\sin 2 x+C \)
(B) \( \frac{x^{3}}{3}-x^{2} \sin x-\cos 2 x+C \)
(C) \( \frac{x^{3}}{3}-x^{2} \cos x-\cos 2 x+C \)
(D) none of these
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