This is what I came up with:
% Generate some example data
mu1 = -0.5; sigma1 = 0.7; mu2 = 0.8; sigma2 = 0.5;
x = linspace(-8, 8, 500);
y1 = normpdf(x, mu1, sigma1);
y2 = normpdf(x, mu2, sigma2);
% Plot it
figure; plot(x, [y1; y2])
hold on
% Detect intersection between curves; choose threshold so you get the whole
% intersection (0.0001 should do unless your sigmas are very large)
ind = y1 .* y2 > 0.0001;
% Find the minimum values in range
minVals = min([y1(ind); y2(ind)]);
if ~isempty(minVals)
area(x(ind), minVals)
end
I don't know if this is the best way to do what you want, but it seems to work.