Remember after one integration you get a formula with a constant of integration, and when you integrate that, you get the double integral plus the integral of the constant of integration, plus a second constant of integration. And the integral of the first constant of integration is the constant times the variable of integration.
Your plot shows a linear trend. That is the constant of integration multiplied by time.
Your blue plot is therefore one of the mathematically correct solutions.
If it is not the solution you want then you need to adjust the constant of integration.
Note that mathematically, trapz(x, y) with equidistant x, is equivalent to (sum(y) - (y(1)+y(end))/2) * delta x
cumtrapz with constant x difference effectively proceeds step by step, taking the proceeding result and adding half of the previous y value and half of the current y value. Those halfs have an influence.