The volume of the solid whose base is the square in the x y- plane 
[0,1] ×[1,2] and whose height is the function f(x,y) = (x^2)y is represented by the double integral, or nested integral (∫_0^1)(∫_1^2)(x^2)y dy dx =(∫_0^1)((∫_1^2)(x^2)y dy) dx .  Note that this base is "simple".

RegionPlot3D[z<x^2*y ,{x,0,1},{y,1,2},{z,0,3},Mesh->None,PlotRange->{{-1,2},{0,3},{0,2}},AxesOrigin->{0,0,0},Boxed->False,BoxRatios->{1,1,.5},AxesLabel->{x,y,z}]