Since the student is specifically using
the left endpoint for every subinterval
height, the method is a Left Riemann
Sum. The Definite Integral represents
the exact area achieved as the number
of rectangles approaches infinity, rather
than an estimation method using a finite
number of rectangles.

For a function 𝑓(𝑥) that is increasing on
an interval [𝑎,𝑏], a left Riemann sum uses
the function's value at the left endpoint of
each subinterval to determine the height
of the rectangle. Since the function is
increasing, the value at the left endpoint
will be the minimum value of the function
within that subinterval, meaning each
rectangle will be entirely below the curve
(or at the same height, in the case of a
constant function). Therefore, the sum of
the areas of these rectangles will always
provide an underestimate of the true area
under the curve.

Since the problem explicitly states
that the height is taken from the middle
of each subinterval, it refers to the
Midpoint Riemann Sum; it is where the
height is determined by the function
value at the exact center (midpoint) of
each subinterval.

The Right Riemann Sum uses right
endpoints. With 5 subintervals, we use:

f(x1), f(x2), f(x3), f(x4), f(x5)

Then, we multiply their sum by:

∆x

The area of each rectangle in a
Riemann sum approximation of a
velocity-time graph is calculated by
multiplying its height (vertical axis value)
by its width (horizontal axis value).
The height of the rectangle represents the
velocity (or speed) of the car at a specific
moment within the time interval (e.g., left
endpoint, right endpoint, or midpoint).
Since the calculation for each rectangle is
essentially velocity×time, and we know
that distance=velocity×time, the resulting
value for each rectangle's area is the
approximate distance traveled during that
specific small time interval. The sum of all
these rectangle areas (the Riemann sum)
approximates the total distance traveled
over the entire duration.