I am reading "Fundamental of Aerodynamics " by J.D.Anderson Fifth edition, At pages 177 and 178 (section 2.14 Stream funciton), the book said: given 2D steady flow, from: $$\frac{dy}{dx}=\frac{v}{u}$$ with u and v are known function of x and y, then we obtain f(x,y) = c by intergration.
If we have steamline 1 is f(x,y) = c1 and streamline 2 is f(x,y) = c2, then why is the mass flow between two streamlines equal (c2 - c1)? The book said that but there is no derivation of that.