Is this formula derivation is true for CES function in continus form or not ?

\lim_{n \rightarrow \infty} \frac{1}{n}\sum_{j=0}^{n} Y_{j,t}^{\frac{\psi -1}{\psi}} = \int_{0}^{1} Y_{j,t}^{\frac{\psi -1}{\psi}} dj

My question is originally about the integral form derivation of CES function in Dixit-Stiglitz(1977) function in new keynesian DSGE models.

Altough CES original form in Macroeconomic books is in a discrete form and as I know Dixit-Stiglitz aggregator function in their original paper is in CES discrete form.