Let \( \mathrm{f} \) be a differentiable function satisfying \( \in...

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Let \( \mathrm{f} \) be a differentiable function satisfying \( \int_{0}^{f(x)} f^{-1}(t) d t-\int_{0}^{x}(\cos t-f(t)) d t=0 \) and \( f\left(\frac{\pi}{2}\right)=\frac{2}{\pi} \)
\( \mathrm{P} \)
The value of \( \int_{0}^{\pi / 2} f(x) d x \) lies in the interval
(1) \( \left(\frac{2}{\pi}, 1\right) \)
(2) \( \left(1, \frac{\pi}{2}\right) \)
(3) \( \left(\frac{3}{2}, \frac{\pi}{2}\right) \)
(4) \( \left(0, \frac{2}{\pi}\right) \)
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