x = sort(rand(1,20));
y = exp(sin(2*pi*x));
yint = cumtrapz(x, y);
plot(x, y, 'k', x, yint, 'b')
syms X B
Y = exp(sin(2*pi*X));
Yint = int(Y, X, 0, X);
fplot([Y, Yint], [0 1])
This illustrates that you can use trapz() with irregular spacing, and that if the values are close enough, it will approximate the true integral.
If you only want to integrate over a particular range, then find the endpoints of the range in the data and only do that portion:
mask = pi/10 <= x & x <= 2*pi/10;
px = x(mask);
py = y(mask);
pyint = cumtrapz(px, py);
plot(px, py, 'k', px, pyint, 'b')
The reason this does not look the same is that you are not bringing in the accumulated value from 0 to pi/10, and definite integration always starts at 0.
