Try this:
x=0:0.1:3.14;
y=sin(4*x).*sec(3*x);
yy = zeros(1,length(x));
yy(:) = 0;
y1=-20:0.1:20;
x1 = ones(1,length(y1));
x1(:) = 0.5;
area_1 = trapz(x(x<=0.5), y(x<=0.5)); % Calculate ‘Area #1’
xc = find((y .* circshift(y, [0 1])) < 0); % Define ‘y’ Zero-Crossings
idx_rng = xc(1)-1:xc(1); % Index Range Including Zero-Crossing
x0 = interp1(y(xc(1)-1:xc(1)), x(xc(1)-1:xc(1)), 0); % Find ‘x’ At Zero Crossing
area_2 = trapz([0.5 x0], [y(x == 0.5) 0]); % Calculate ‘Area #2’
plot(x,y,x,yy,'--',x1,y1,'--')
hold on
ha1 = area(x(x<=0.5), y(x<=0.5), 'FaceColor','g');
ha2 = area([0.5 x0], [y(x == 0.5) 0], 'FaceColor','r');
hold off
A1str = sprintf('Area 1 = %6.3f', area_1);
A2str = sprintf('Area 2 = %6.3f', area_2);
legend([ha1 ha2], A1str, A2str)
I colored ‘area2’ for clarity, and to show the value in the legend. Make whatever changes you need to. Note that this code is specific to your Question as you posted it, and while the ideas will generalise to similar applications, the code itself will not.
