Suppose I have an SDE, for example
$dN=rdt + adB$
for constants a and r, as in Oksendal chapter $5$. He take the "integral" of this and ends up with,
$N=rt + aB$.
without regard or mentioning what is going on. Sure integration is inverse of differentiation. But these objects above are not the same differentiation. The first being a Riemann or Lebesgue and the second an Ito integral. So how does one make sense of this?
The symbolic expression $dN=r\,dt+a\,dB$ is defined to correspond to the integral equation $$ N_t-N_0=\int_0^tr\,ds+\int_0^ta\,dB_s $$ which in the case of constant coefficients can directly be integrated in the Riemann resp. Ito sense.
In short, your question is not.