Let \( f(x)=x^{3}+a x^{2}+b x+c \) where \( a, b, c \) are real numbers. If \( f(x) \) has local....

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Let \( f(x)=x^{3}+a x^{2}+b x+c \) where \( a, b, c \) are real
\( \mathrm{P} \)
numbers. If \( f(x) \) has local minimum at \( x=1 \) and a local maximum at \( x=-1 / 3 \) and \( f(2)=0 \), then
(1) \( f(x)=x^{3}-x^{2}-x+2 \)
(2) \( f(x)=x^{3}-x^{2}-x-2 \)
(3) \( f(x)=x^{3}+x^{2}+x-2 \)
(4) If \( F(x)=\int f(x) d x \), then \( F(1)-F(-1)=\frac{-14}{3} \)
.


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