The additive interval property says we can break up integrals into pieces (integrals on smaller intervals with the same integrand). Specifically, the integral over the interval [a,c] is the same as the sum of the integrals over [a,b] and [b,c] when a≤b≤c. You can visualize this in terms of areas under the curve y=f(x). Also, the property still makes sense even when a,b,c are not increasing in order, but we'll need to define backwards integrals for that.