% This approximates integrals of a function of two variables f(x,y)
% on a rectangle: a<x<b, c<y<d, using an m by n grid of evenly spaced
% subrectangles. On each subrectangle, the function f(x,y) is evaluated
% at the lowerleft corner. 
%  
function I = lowerleft(f,a,b,c,d,m,n)
h = (b-a)/m;                            %step size in x direction
k = (d-c)/n;                            %step size in y direction
sum = 0;             
x = a;                                  % x begins at a
for i = 1:m                             % x loop
y = c;                                  % y begins at c
    for j = 1:n                         % y loop
        sum = sum + f(x,y);
        y = y + k;                      % y steps by k
    end  
    x = x + h;                          % x steps by h
end
I = sum*h*k;