Pensieve header: Integration by Riemann sums.

f=2-(x^2)-(y^2); Δ=0.2;
GraphicsRow[{
Plot3D[f, {x,-1,1}, {y,-1,1}, Mesh -> False,ViewPoint->{2.90291,-1.43548,0.981093},ViewVertical->{0.,0.,1.}],
DiscretePlot3D[f, {x,-1,1,Δ}, {y,-1,1,Δ},  ExtentSize -> Full, PlotStyle -> Yellow, ViewPoint->{2.90291,-1.43548,0.981093},ViewVertical->{0.,0.,1.}]
}]