Observe the graph: The area is bounded between
and
.
The number of subintervals are
.
The width of the subintervals is
.
From the graph approximate the function values.
\
and
.
Find the upper sum.
\The maximum value on each subinterval occurs at the right end point.
\
.
Right end points of the graph are
and
.
The upper sum(
).
The upper sum is
.
Find the lower sum.
\The minimum value on each subinterval occurs at the left end point.
\
.
Left end points of the graph are
\
and
.
The lower sum is
.


The lower sum
.
The area of the shaded region falls between
square units and
square units.
The area of the shaded region falls between
square units and
square units.