The upper sum is an approximation of the area under a curve using the sum of the areas of rectangles that overestimate the region. Each rectangle's height is determined by the maximum function value over a subinterval.
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Upper sums are used to approximate definite integrals from above.
The interval $[a, b]$ is divided into $n$ subintervals for calculating upper sums.
The height of each rectangle in the upper sum corresponds to the supremum (maximum) value of the function within that subinterval.
As $n$ approaches infinity, the upper sum approaches the exact value of the integral if the function is integrable.
Upper sums are often compared with lower sums to establish bounds for Riemann sums.