I need to prove the following integral relation:
$$\lim_{T \to (1-i \epsilon) \infty} \mathrm{\int_{-T}^T dt_1 dt_2 e^{-ia |t_1|} \cdot e^{-ib |t_2|} \cdot e^{-ic |t_1-t_2|}} = \frac{-2}{(a+b)(b+c)} + \frac{-2}{(a+b)(a+c)} + \frac{-2}{(a+c)(b+c)}$$
I tried to use Fubinis theorem, so to integrate over $t_1$ first and evaluate and to integrate over $t_2$ then, but I'm getting stuck with the modulus $|t_1 - t_2|$. I'm not really sure what cases I need to check and there fore how to split this integral. I'm very grateful for all advices!