Mathieu,
Looking at the IntegratePolygon it looks like it is just breaking each polygon down in to triangles to calculate the areas. I have used this functionality in the past to get an idea whether my lift and drag calculations were close and was concerned that it was missing out all the polygons.
I am using v5.2.0 currently and I saw this post, and wondered if the cellsize was a feature in a newer version that solves this problem.
Thank you for your help, Ian