You could use trapz to calculate the area under the curve.
But before that you need to calculate the intersecting portion of the curves. Check this example with some dummy data,
x1 = 0.01:0.01:1;
y1 = [sin(pi*x1) zeros(1,20)];
x2 = x1+0.2;
y2 = [zeros(1,20) sin(pi*x1)];
y_d = [y2(y2<y1) y1(y1<y2)];
area_int = trapz(y_d)
%plots in case you want to visualize
plot(y1)
hold on
plot(y2)
plot(y_d,'k-o')
