Gauss's law states that the total electric flux P through any closed surface is equal to the total charge enclosed by that surface.

Thus

$\psi = Q_{enc}$...(1)

that is,

$\Psi=\oint d \Psi=\oint_{S} \mathbf{D} \cdot d \mathbf{S}$...(2)

= Total charge enclosed $Q=\int \rho_{v} d v$

or

$\boxed{Q=\oint_{S} \mathbf{D} \cdot d \mathbf{S}=\int_{v} …