The total flux through a surface S can be defined as follows: $\iint_{S}\left(\vec{F}\cdot\vec{n}\right)\,dS$ (Eq. 1)
Some text books appear to use a different notation: $\int_{S}\left(\vec{F}\cdot\vec{n}\right)\,dS$ (Eq. 2)
Is Eq. 2 just a more compact notation of Eq. 1, or do both equations actually differ? Thank you!