Calculating a complex integral How can I calculate $$\int_{|z-i|=1}\frac{1}{z+i}\;dz$$

It seems like the non-continuous point is: $z=-i$, and it is not inside the contour, would that mean that the integral is simply zero?

Thanks
Yes

Hint : Use Cauchy-Goursat Theorem
Cauchy Integral formula gives us
\begin{align}
f(a) = \oint_\gamma \dfrac{f(z)}{z-a} \,dz
\end{align}

Let $f(z) = 1 \; \forall z \in \mathbb{C}$, so, you are evaluating $f(-i)$, which by our definition is 1.