I am reading the book "Riemann's Zeta Function" by H. M. Edwards. I had a confusion in Section 1.6, Page 13 at a proof of the functional equation of Riemann Zeta Function.
It has been derived from the contour integral $$\zeta(s)=\dfrac{\Pi(-s)}{2\pi i}\int^{+\infty}_{+\infty}\dfrac{(-x)^s}{e^x-1}\dfrac{dx}{x}$$
Let $D$ denote the domain in the s-plane which consists of all points other than those which lie within $\epsilon$ of the positive real axis or within $\epsilon$ of one of the singularities $x=\pm2\pi in$ of the integrand of. Let $\delta D$ be the boundary of $D$ oriented in the usual way. Then, ignoring for the moment the fact that D is not compact, Cauchy's theorem gives $$\dfrac{\Pi(-s)}{2\pi i}\int_{\delta D}\dfrac{(-x)^s}{e^x-1}\dfrac{dx}{x}=0$$
I don't have any confusion up to here.
Now one component of this integral is the original contour integral with the orientation reversed, whereas the others are integrals over the circles $|x\pm 2\pi in|=\epsilon$ oriented clockwise. Thus when the circles are oriented in the usual counter clockwise sense, it becomes $$-\zeta(s)-\sum\dfrac{\Pi(-s)}{2\pi i}\int_{|x\pm 2\pi in|=\epsilon}\dfrac{(-x)^s}{e^x-1}\dfrac{dx}{x}=0$$
I get how the integral has been split but, I'm not sure how the orientations are determined as reversed.
The rest of the derivation is quite clear to me but, I'm really confused about the orientations.