This applet provides a conceptualization of Riemann sums and their limit (definite integral) as area under a function. Note that the Left and Right sum contain the indices (i-1) as a result of "counting" or "labeling" the partitions of the interval.
The type of sum and number of partitions can be adjusted to show the effect of partition size on the approximation. Further discussion incorporating this applet may include conditions for which Riemann sums under- or over-estimate the true area, as well as the implications of the First Fundamental Theorem of Calculus (Definite integral = f(b) - f(a)).
