JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 7

Let $f:\mathbf R\to\mathbf R$ be a differentiable function such that $f\left(\dfrac\pi4\right)=\sqrt2$, $f\left(\dfrac\pi2\right)=0$ and $f'\left(\dfrac\pi2\right)=1$ and let $g(x)=\displaystyle\int_x^{\pi/4}\left(f'(t)\sec t+\tan t\sec t\,f(t)\right)dt$ for $x\in\left[\dfrac\pi4,\dfrac\pi2\right)$. Then $\displaystyle\lim_{x\to\left(\frac\pi2\right)^-}g(x)$ is equal to :