Hello everyone! This problem was given to me last week. I've have never ever learned fourier analysis, but my profesors aren't aware of this fact. So this is the problem, and I would be very grateful for any help, especially drawing graph of fourier transformation. Thank you.

$\displaystyle f(t)=\begin{cases}

{1}-{t}^{2} & , |t|<1 \\

0 & , |t|\geq1

\end{cases}$

Find Fourier tranformant ($\displaystyle F(t)(\omega)$) of function f(t) and draw graph of fourier transformant.

P.S.I'm sorry for my english, it's not pretty good