Integration Over Polygons

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I'm looking for an open source alternative to Mathematica that provides an easy way to integrate functions over polygons. In Mathematica I can define a polygon R and integrate some function f(x,y) over it with a single command without having to determine the bounds of integration on x and y:

Integrate[f(x,y),{x,y}∈R]

Is it possible to do this type of integration in Sage? The polygons I need to integrate over have hundreds of vertices, so doing it piece-wise is not an option.