[wildrabbitt]

Hi, can anyone explain this?



\[S=\sum_{v=-\infty}^{\infty}\int_0^Ne^{2\pi ivx+2\pi i\frac{x^2}{N}} \mathrm{d}x\]
\[=N\sum_{v=-\infty}^{\infty}\int_0^1e^{2\pi iN(x^2+vx)} \mathrm{d}x\]


What I'm hoping for is some intermediate steps which get from the first, step by step to the second that make sense.


Please help.