Lời giải

Đặt \( t = -x \):  
\( I = \int_{-\alpha}^{\alpha} \frac{f(x)}{a^x + 1} \, dx = \int_{-\alpha}^{\alpha}
\frac{f(-t)}{a^{-t} + 1} \, dt = \int_{-\alpha}^{\alpha} \frac{a^tf(t)}{a^t + 1} \, dt \)

\( \Rightarrow I = \frac{1}{2} \int_{-\alpha}^{\alpha} f(t) \, dt = \int_0^a f(t) \, dt \)