Calculate partial area under plot

Hi everyone,

I'm trying to calculate the crossed area under this closed graph:

I have a set of X,Y coordinates (red points), in which I plotted the closed graph. And the equation of a straight line of Y = a, which cuts the closed graph at 2 points. My goal is to find the sum of the areas of S, S1 and S2.

For the area of S, I used the polyarea(X,Y) function.

But I can't find a solution to calculate the S1 and S2 area.

Could anyone give me a suggestion, please?

Thank you!