# data[].attributes.body
Left: we expected to see 4 and we did see 4.

Right Expected to see 4 but only saw 3. It's because of the formula delta x = (b-a)/n which determines the width of rectangles we would have and we were only able to fit 3, therefore we are only able to use 3 triangles to do the right Reiman sum.

# data[].attributes.body
a. Expect to see 4, but we see 3. Not sure the reason
b. Still 3 rectangles

# data[].attributes.body
expected 4 but only see 3. this is because the first rectangle has an area of zero.

# data[].attributes.body
a.4, 3
b.3

# data[].attributes.body
Left points: 3 rectangles
Right points: 3 rectangles

# data[].attributes.body
a) 3
b) 3

# data[].attributes.body
If Left hand reiman sum is an overestimate since some of the rectangles shapes go outside the curve.

Right hand is an underestimate since rectangles are under the curve and does not fully cover the area of the curve.

# data[].attributes.body
a. 3 rectangles for one rectangle has a height of 0 at a=-3.
b. still 3 rectangles

# data[].attributes.body
c. n not smaller than 4 for 16/3=5.333... so the sum of area of rectangles have to be smaller than 6.333...
d. any value

# data[].attributes.body
I mean we are talking four units from a=-3 and b=1

# data[].attributes.body
c) n=4
d)n=11

# data[].attributes.body
when n=4, sum =6.25, which is within one unit of 16/3=5.3
d. n=5 sum=4.48

# data[].attributes.body
The signed area between the x-axis and the curve between x = -0.5 and x =2 will be positive

# data[].attributes.body
Righthand is overestimate and lefthand is underestimate

# data[].attributes.body
c. n>=4
d. any positive integral

# data[].attributes.body
a. underestimates for there is always area that below the curve is not counted.
b. overestimates for there is always area that above the curve is counted.

# data[].attributes.body
negative for the area below x-axis are marked negative on the GeoGebra, though it should be positive for area is always positive