I want to calculate the line integral of a function $f$ for the line from 0 to 1. We defined the line integral as $\int_\gamma f(t)dt=\int_a^b f(\gamma)\gamma'dt$ for a continuous $\gamma:[a,b]\to\mathbb C$.
I have trouble understanding what exactly $\gamma$ is in my case. Obviously it's a continous function $[0,1]\to\mathbb C$, but how do I continue here?
$\gamma$ refers to a parameterization of the curve along which you are integrating. Here, you are integrating along the line from $0$ to $1$, so you must parameterize this line. One parameterization of this line is $$ \gamma(t) = t, \qquad 0 \leq t \leq 1.$$