I would like to derive the Fourier transform of a function given by
$$f(x) = \begin{cases} x^2, & -1 < x < 1 \\ 0, & \text{Elsewhere} \end{cases}$$
I derived it by defining the Fourier transform as
$$F(k) = \int^{\infty}_{-\infty} f(x) \exp(ikx) dx$$
I got
$$\frac{2a^2}{k}\sin(ka) + \frac{4a}{k^2}\sin(ka)-\frac{4}{k^3}\sin(ka)$$
Is that correct?