$\displaystyle a_n=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(t)e^{-int}dt\\$

$\displaystyle \frac{e^{in\pi}}{2\pi}\int_{-\pi}^{\pi}\overline{f(t)}\overline{e^{int}}dt\\$

$\displaystyle =\frac{e^{in\pi}}{2\pi}\int_{\pi}^{-\pi}e^{-i(-n)t}=e^{in\pi}\overline{a_{-n}}$

why there is $\displaystyle \overline{a_{-n}}$??

by the first formula it supposed to be only $\displaystyle a_{-n}$

i understand how they removed the conjugat of exponenet

but i cant see how they removed it from the f part