I am confused about this thing
The definition of the Fourier transform of a function $f \in \mathbb{L}^1( \mathbb{R})$ (integrable function ): $$F(f)(x)=\int_{-\infty}^{\infty}f(x)e^{-i2\pi xt}dt$$ but if I want to compute the fourier transform of a periodic function ($f(x)=\sin(x)$ for example ) what i have to do 1) consider
$f(x)=\sin(x)$ for $x \in [0,2\pi]$
$ f(x)=0 $ else
2) compute the fourier trannformation of $\sin(x)$ as a function definied on $ \;\mathbb{R} (f(x)=\sin(x) $ for all $x \in \mathbb{R})$