python – solve and integration differential problem c++

I want to write c++ code that first numerically compute dy/dt=f(y,t) and then after that evaluate
integration as form g(t)=h(t)+y(t)…that y is solution of ode that introduce as dy/dt=f(y,t) and h is function of t for example h(t)=t.
and bound for integration is a and b. integration(g(t),a,b)