Difference Equation: Explained & Derived - QM1

[Domnu]

In the following link: http://electron6.phys.utk.edu/QM1/modules/m2/square_potentials.htm what does the difference equation mean, and how is it gotten from the previous step?

 

[George Jones]

Rearranged slightly, the equation above it is

$$\frac{\partial^2 \phi_\epsilon \left( x \right)}{\partial x} = \frac{2m}{\hbar^2} \left( V_\epsilon \left( x \right) - E \right) \phi_\epsilon \left( x \right).$$

What happens when you integrate both sides of this equation from $x = x_1 - \epsilon$ to $x = x_1 + \epsilon$?