Assumptions
closed interval =
Partition
A partition of
nodes
Length
If
then is called the length
Notation
Let
Notice
Lower Riemann sum
Let
for in , this is Lower Riemann sum
Upper Riemann sum
this is Upper Riemann sum
Theorem
Remark
Clearly
[a,b]
Lower Riemann Integration
Upper Riemann Integration
Riemann integral
A bounded function
is Riemann integral