If \( f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2}x\frac{\pi}{2} \), and \( f(0)=0 \),...

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If \( f^{\prime}(x)=\tan ^{-1}(\sec x+\tan x),-\frac{\pi}{2}x\frac{\pi}{2} \), and \( f(0)=0 \), then \( \mathrm{f}(1) \) is equal to :
P
[JEE Main-2020 (January)]
W
(1) \( \frac{1}{4} \)
(2) \( \frac{\pi+2}{4} \)
(3) \( \frac{\pi-1}{4} \)
(4) \( \frac{\pi+1}{4} \)
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