/sci/ - Science & Math

So I'm kinda lost.
Covering magnetic fields, and one of the first formulas I get is for flux.
[math]flux = \int_c BdS,[/math]
(B is magnetic induction, S is the area of the contour, might be translating these somewhat wrong)
Okay, seems reasonable enough, but next chapter it says the law of conservation is:
[math]\int_c BdS = 0, [/math]
Does this mean that the flux is always equal to zero? I mean, I know it doesn't, but what am I missing here?