When solving a variables separable ODE such as:
dy/dx=f(x) => intergral dy = integral f(x) dx
what limits does one integrate between??????
If the boundary condition is given, then
.
If the boundary condition is given and the the value of y when is required, then
.
Otherwise there are no limits:
and the right hand side is an indefinite integral. Of course, this approach can also be taken when boundary conditions are given - see the next reply.