b(t) = 
The initial conditions on the integrators need to be set to appropriate values to yield the expected result.
Define the yellow curve
syms t
y(t) = sin(t);
The blue curve is the antiderivative of the yellow curve with some constant of integration to be determined
syms C1
b(t) = int(y(t),t) + C1
Same for the red with respect to blue
syms C2
r(t) = int(b(t),t) + C2
Now solve for the Ci based on the initial conditions for r(t) and b(t), which are both zero based on the scope plots
sol = solve([b(0)==0,r(0)==0],[C1,C2])
Sub back to get the final results for b(t) and r(t)
b(t) = subs(b(t),sol)
r(t) = subs(r(t),sol)
which looke like they match the plots in the scope.
