Whereabouts of \(g\).

Level pending

Let \(f(x)=(1-x)^2 \sin^2 x+x^2\) for all \(x \in \mathbb{R}\), and let \(g(x)=\int_{1}^{x}\left ( \frac{2(t-1)}{t+1}-\ln t \right )f(t)dt\) for all \(x \in (1, \infty)\).

Which of the following is true?

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