A contour integral follows a path in the complex plane and accumulates the complex function values along that path. The parameterization $z(t)$ tells the calculator where the path goes and how quickly it moves.

The calculator rewrites $int_C f(z),dz$ as a standard integral in the parameter $t$, which is why both the contour expression and the bounds matter.

The path preview is not decorative. It is the quickest way to verify orientation, start and end points, and whether your contour matches the intended geometry.