1. Definite Integrals
The definite integral  of a function  defined on the interval  is given by

where  is a point in the th subinterval of the partition

of the interval , , and . The sum

is called a Riemann sum. The function  is integrable on  if the preceding limit exists.
If  is integrable on , then

2. Matrix Equations
The system of equations

contains the same information as the following matrix equation: