Definition (Definite Integral): Let be continuous on the closed interval

Riemann-Darboux Sums

Def: P is said to be a partition of the closed interval if P is a finite subset of which contains both a and b.
You may index the elements of P so that if , you may conclude that
Def: Let be a partition of . We define

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  called the width of the subinterval
  
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  called the norm or mesh of the partition P.
  

Def: A partition is said to be a regular partition of if, for some , In this case,

Def: Let f be a function bounded on and a partition of . By a Riemann sum of f over ¸ we mean the sum represented by ¹ and defined by

any choice of ,