Hi all, reading a paper i struggled over the following formula:

$\displaystyle $\zeta_T(v) = \int_{-\infty}^0 dk e^{ivk} e^{-rT}\int_{-\infty}^k (e^k - e^s)q_T(s)ds + \int_{0}^{\infty} dk e^{ivk} e^{-rT} \int_{k}^{\infty} ( e^s- e^k)q_T(s)ds$$

then they claim changing the order or integration should result in

$\displaystyle $\zeta_T(v) = \int_{-\infty}^0 ds e^{-rT} q_T(s) \int_{s}^{\infty *} (e^{(1+iv)k} - e^s e^{ivk})dk + \int_{0}^{\infty} e^{-rT} q_T(s) \int_{0}^{s} ( e^s e^{ivk}- e^{(1+iv)k})dk$$

What I dont get is why the first inner integral marked by * goes from s to $\displaystyle $\infty$$ and not from s to 0. Can someone explain this to me? thx in advance.