Answer
See explanation.
Work Step by Step
(a) $F^{\prime}(x)=-3+3 x^{2}$
(b) $F(x)=\int_{1}^{x}\left(-3+3 t^{2}\right) d t=\left(-3 t+t^{3}\right)_{1}^{x}=-1+3+x^{3}-3 x=2-3 x+x^{3}$
Differentiating then gives $F^{\prime}(x)=-3+3 x^{2}$
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