Suppose $\displaystyle {f{{\left({x}\right)}}}$ is decreasing, with $\displaystyle {f{{\left({3}\right)}}}={25}$ and $\displaystyle {f{{\left({23}\right)}}}={15}$.

Consider the region under the graph of $\displaystyle {y}={f{{\left({x}\right)}}}$, above the $\displaystyle {x}$-axis, and over the interval $\displaystyle {3}\le{x}\le{23}$.

If we use $\displaystyle {n}={1}$ partitions, then the left sum will be Preview Question 6 Part 1 of 5   , which will be Select an answer greater than less than equal to the actual area.

The error in using this as our approximation to the area will be less than or equal to Preview Question 6 Part 3 of 5   square units.

If we use $\displaystyle {n}={2}$ equal-width partitions, then the error in using the left sum will be less than or equal to Preview Question 6 Part 4 of 5   square units.

If we use $\displaystyle {n}={4}$ equal-width partitions, then the error in using the left-sum will be less than or equal to Preview Question 6 Part 5 of 5   square units.