For a given surface the Gauss’s Law is stated as $\text{∮}\mathrm{E}\cdot \mathrm{ds}=0$. From this we can conclude that :

Given data:

Gauss law defines

Concepts used: Gauss Law

Detailed answer:

Gauss' law states that the total electric flux arising from a volume of charge is equal to the trapped charge multiplied by the dielectric constant of the medium within the surface.

So if $\int E.ds=0$, this means that the net flux through the surface is zero.