Definite Integral : Given a function f ( x ) which is continuous on the interval [a,b] we divide the interval in n subintervals of equivalent width, Δx , and from each interval select a point x_i* .  Then the definite, integral of f(x) from a to b is

There is also a little bit of terminology that we should get out of the way here.

Lower limit of the integral

The number "a" that is at the bottom of the integral sign is called the lower limit of the integral

Upper limit of the integral

The number "b" at the top of the integral sign is called as the upper limit of the integral. 

Interval of integration

Also, in spite of the fact that a & b were given as an interval the lower limit does not essentially need to be smaller than the upper limit.  Jointly we'll often call a & b the interval of integration.