TITLE: calculate $\int_{0}^{i} e^z\, dz$
QUESTION [5 upvotes]: calculate $\displaystyle\int_{0}^{i} e^z\, dz$
Could someone help me through this problem?

REPLY [5 votes]: The function $e^z$ is entire. Hence, contour integrals are independent of path. The antiderivitive of $e^z$ is just $e^z$. Stick in the endpoints, and do the subtraction.