The function is , .

Here and .

Number of subintervals are .

Width of the interval is .

Let the Sample points be right end points.

Right end points are and .

Riemann sum is , where .

Riemann sum is .

Graph :

Graph the Riemann sum.

The Riemann sum represents the sum of the areas of the three rectangles above the axis minus the sum of the areas of the two rectangles below the axis.

Riemann sum is net area of the rectangles with respect to axis.

(b)

Let the sample points be mid end points.

Number of subintervals are .

Width of the interval is .

Mid points are and .

Riemann sum is , where .  \ \

Riemann sum is .

Graph :

Graph the Riemann sum.

The Riemann sum represents the sum of the areas of the four rectangles above the axis minus the sum of the areas of the two rectangles below the axis. 

Riemann sum is net area of the rectangles with respect to axis. 

(a) Riemann sum with right end points is .

(b) Riemann sum with mid points is .