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

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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

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