I'd like to calculate the total area of several polygons along a north-south axis. A bit like this http://www.closr.it/canvas/1307/#/spot

There is a similar question with R : Spatial graphing, distribution of polygon area over latitudes . But I was wondering if there was not a simpler solution with QGIS, and if possible in a continuous way, not a discrete one.
Rcode at http://gis.stackexchange.com/a/33449 will give you your continuous solution. The code conducts a vertical (north-south) line sweep, finding its intersection with a polygon (or, just as easily, a set of polygons). You simply want to track the total length of the intersection. When you use a cylindrical equal-area projection, these lengths are exactly what you want to be plotting in your graph (which does not actually show total area: it is the area density per unit distance north-south). – whuber Jun 05 '15 at 16:37