You are using the loop incorrectly, and you don't need it anyway. You are doing an integration over a single point, which is unlikely to work in any context. You could sum the values and divide by the delta x, but by not using array operations you're not taking advantage of the full potential of Matlab.
The method I show below will have a rounding error that increases with the number of crossings, but it shouldn't get too bad, especially if you're using a finer x scale.
% lprofile=xlsread(fname_lprofile);
% x1=lprofile(:,1);
% y1=lprofile(:,2);
% y2=lprofile(:,3);
% plot(x1,y1,x1,y2)
%generate random data instead
x1=linspace(0,2*pi,300);
y1=cos(x1);
y2=sin(x1);
plot(x1,y1,x1,y2)
low=y1-y2;low(low<0)=0;
hi=y2-y1;hi(hi<0)=0;
A_low=trapz(x1,low);
A_hi=trapz(x1,hi);
