[NBHM PhD Screening Test_2006_Analysis]
Find all possible values of $\displaystyle I= \int_C \frac{dz}{1+z^2}$, where $C$ is a curve with initial point $0$ and final point $1$ that does not meet the poles of $\dfrac{1} {1+z^2}$
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It looks like a problem related to residue theorem, but I have no idea what should I do as $C$ is not closed. Can anyone provide some hints? Thanks!