Gauss Law is defined as "The total of the electric flux out of a closed surface is equal to the charge enclosed divided by the permittivity. The electric flux through an area is defined as the electric field multiplied by the area of the surface projected in a plane perpendicular to the field." ("Gauss's Law." Gauss's Law. N.p., n.d. Web. 31 Jan. 2017.) COLERA helped us to understand these principles.
The integral of the function above came out to -pi. (-3.141592653)
Above we have a 3D view of a dipole, with an integal of nearly 0.