I was watching this 3Blue1Brown video about Fourier series https://youtu.be/r6sGWTCMz2k (timestamp: 16:30) and the presenter mentioned that to get the average position of a curve in the complex plane (which he describes as a sort of center of mass) you need to integrate the complex function that "draw" the curve with respect to "time" (a parameter). I don't understand why that makes sense. Could someone help me see the connection?
EDIT: The thing that i do not understand is why should this integral: $$\int_0^1 f(t) \, dt$$ (Where $f(t)$ is a complex function that, as $t$ ranges from $0$ to $1$, describes a curve in the complex plane) Represents the avarage position of points / "center" / "center of mass" of the drawing.
I understand why this average position can be a kind of center of mass and I understand why the curve is described by this $t$ parameter. What confuses me is just the fact that the integral shown above precisely gives the complex number associated with the center of mass of the curve.
Image from the 3b1b video (modified)