\[ \int_{-\pi / 2}^{\pi / 2}\left(\frac{1}{(2023)^{x}+1}\right) \cdot \frac{\sin ^{2022} x}{\sin...

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\[
\int_{-\pi / 2}^{\pi / 2}\left(\frac{1}{(2023)^{x}+1}\right) \cdot \frac{\sin ^{2022} x}{\sin ^{2022} x+\cos ^{2022} x} d x
\]
(a) \( \frac{\pi}{4} \)
(b) \( \frac{\pi}{5} \)
(c) \( \frac{\pi}{9} \)
(d) \( \frac{\pi}{7} \)
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