integration - Evaluating $int_{-infty}^{infty} frac{xsin(kx)}{x^2+a^2} ,mathrm dx$ using complex analysis

I'm trying to solve the following integral:

$$\int_{-\infty}^{\infty} \frac{x\sin(kx)}{x^2+a^2} \,\mathrm{d}x$$

I don't really have any idea where to start. The previous parts of the question involved complex numbers and Cauchy's Integral Formula, however I can't think how I'd applying that here.

Any help would be greatly appreciated :)