Parametric Centroid Problem

So one of the things I have to know for my Calc final is how do find the center of mass of a centroid given its parametric formulas. We learned how to find centers of mass and how to use parametric equations but never put the two together in class.

So how would I go about solving a problem like this:

Find the y-coordinate of the centroid oft he curve given by the parametric equations:

x=(3^(1/2))t^2

y=t-t^3

t= [0, 1]

I can figure out most of it, I'm just stuck trying to figure out how I would find the area of the centroid

Thanks :)