Let \( f: R \rightarrow R \) be defined as \( f(x)=\int_{0}^{x}\lef...

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Let \( f: R \rightarrow R \) be defined as \( f(x)=\int_{0}^{x}\left(\sin ^{2} t+1\right) d t \) and \( g \) is the inverse function of \( f \),
\( \mathrm{P} \) then \( g^{\prime}\left(\frac{3 \pi}{4}\right) \) is equal to :

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(a) \( \frac{4}{3 \pi} \)
(b) \( \frac{4 \pi}{3} \)
(c) \( \frac{1}{2} \)
(d) 1
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