I need to calculate the area enclosed in a two-dimensional listplot and following an answer to a similar question I tried this way:

 imgnorm = (mnorm = 
 MorphologicalComponents[
 Erosion[Binarize[
 ListLinePlot[{list}, ImageSize -> Large, Axes -> False]], 
 0.5]]) // Colorize

 listareas = {area1 = 1/. ComponentMeasurements[{mnorm, imgnorm}, "Area"], area2 = 2/. ComponentMeasurements[{mnorm, imgnorm}, "Area"]}

It works fine, however it is not precise enough for what I need to do because part of the area is taken by the black line.

The list is quite big and the points don't form a polygon.

Any help would be appreciated, thank you in advance.