Fourier transform of $1/(x^2+m^2)$ by residues

Compute \(\int _ { - \infty } ^ { \infty } { \frac { e ^ { i \alpha x } } { x ^ { 2 } + m ^ { 2 } } }\) dx with \(\alpha , m \in \mathbb { R }\) (hint: consider the two cases of positive or negative α separately);