Integration from a plot

I need to plot the integral of a function, but I only have the data. I would like to avoid using polyplot and apparently cumtrapz does not work. I just compared with an easy integration. For instance.

x = 0:pi/100;2*pi;

f = sin(x); % imaging this is the given data

g = cumtrapz(x,f); % Integration.

The result should be g = -cos(x), but instead I got g = -cos(x)+1

[Robert U]

The result of the integration should be

g = -cos(x) + A

where A is the integration constant. Since cumtrapz() is the cumulative trapezoidal numerical integration, the boundary condition is set to

g(0) = 0

resulting in

A = 1

Kind regards,

Robert