First part of the question asks me to state the path integral $\int_\gamma f$, which I defined as: \begin{equation} \int_\gamma f = \int^b_a f(\gamma(t))\gamma ' (t) dt \end{equation}
And the second part asks to evaluate the integral \begin{equation} \int _\gamma (e{^z}^{2} + \overline{z}) dz \end{equation} where $\gamma$ is the positively oriented unit circle.
Does this mean that $\gamma(t) = e^t + t \ (0 \leq t \leq 1) $ ?