To understand the meaning of the variables in Gauss's law,

To understand the meaning of the variables in Gauss’s law, and the conditions under which the law is applicable. Gauss’s law is usually written

ΦE=∫E⃗ ⋅dA⃗ =qenclϵ0ΦE=∫E→⋅dA→=qenclϵ0

, where ϵ0=8.85×10−12C2/(N⋅m2)ϵ0=8.85×10−12C2/(N⋅m2) is the permittivity of vacuum.

How should the integral in Gauss’s law be evaluated?
around the perimeter of a closed loop
over the surface bounded by a closed loop
over a closed surface