Use the definition to compute the following integral:

$\displaystyle \int_C e^z$ where $\displaystyle C$ is the contour from $\displaystyle 1-i$ to $\displaystyle 1+i$.

I do not see how to do this problem. I know the definition is $\displaystyle \int_C f(z)dz = \int_C f(z(t))z'(t)dt$. However, I don't see how to use it in this problem. Thanks.