The area bounded by the curve \( y=f(x), x \)-axis, and the ordinates \( x=1 \) and \( x=b \) is...

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The area bounded by the curve \( y=f(x), x \)-axis, and the ordinates \( x=1 \) and \( x=b \) is \( (b-1) \sin (3 b+4) \). Then, \( f(x) \) is
(A) \( (x-1) \cos (3 x+4) \)
(B) \( \sin (3 x+4) \)
(C) \( \sin (3 x+4)+3(x-1) \cos (3 x+4) \)
(D) none of these
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