Deriving Fick's Principle from the Equation of Conservation of Matter I don't know where to start with the following problem:

Can anyone give me any pointers?
(For maximum assistance, please adapt your responses and solutions to be understood by a beginner, prefacing and explaining what you are doing so I can follow along.)

The left- and right-hand sides of the conservation-of-mass equation 
$$\frac{\partial c}{\partial t} = - \frac{\partial q}{\partial x}$$
are assumed to be everywhere-continuous functions of spatial coordinate $x$ and time $t$, with $c$ being the solute mass concentration (density). 
The equation expressing "Fick's Principle" can be derived by fixing $t$ and integrating both sides of the above equation with respect to $x$ over a finite interval, say $[x_1, x_2]$:  
$$\int_{x_1}^{x_2}\frac{\partial c}{\partial t}\, dx = - \int_{x_1}^{x_2}\frac{\partial q}{\partial x}\, dx$$
$$\frac{\partial}{\partial t} \int_{x_1}^{x_2}c\, dx = -(q(x_2,t) - q(x_1,t))$$
$$\frac{\partial }{\partial t}m = q_{in} - q_{out}$$
where $m$ is the solute mass in the interval at time $t$.

For similar derivations in the rather more-complicated case of three spatial dimensions, see continuity equation.
