A
function Φ of the
reals is called a
step function on [a,b]
iff:
For some
finite set of points
a = b
_{0} < b
_{1} < ... < b
_{n} = b
Φ is
constant on the
interval (b
_{i1} , b
_{i}) for i = 1,2,3, ... , n.
In other words, Φ looks like this:

** **
** 
** ** **






The
integral of a step function is given by:
∫ Φ(x)dx =
Σ (b
_{i}  b
_{i})c
_{i}