Then the integral conservation law Eq. 10 can be written

We next use the midpoint quadrature rule to approximate the left side of Eq. 11. That is:

When developing conservation law FDEs, there are three commonly used strategies for using numerical integration to approximate the integral on the right side of Eq. 11:

**Left end-point quadrature:**

**Right end-point quadrature:**

**Midpoint quadrature:**