Let $f(x)=(1-x)^2 \sin ^2 x+x^2$ for all $x \in$ IR and let $g(x)=\int_1^x\left(\frac{2(t-1)}{t+1}-\ell\right.$ nt $) f(t) d t$ for all $x \in(1, \infty)$.
Which of the following is true ?
Select the correct option:
A
g is increasing on $(1, \infty)$
B
g is decreasing on $(1, \infty)$
C
g is increasing on $(1,2)$ and decreasing on $(2, \infty)$
D
g is decreasing on $(1,2)$ and increasing on $(2, \infty)$
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