(a)

Determine  using right endpoints.

Observe the graph of .

Number of subintervals are .

Width of the interval is :.

Right end points are  and .

Riemann sum is .

.

Substitute corresponding function values in above expression observe from the graph.

Area under the graph of the function using right endpoints is .

.

(b)

Determine  by left end points:

Number of subintervals are .

Width of the interval is  :.

Left end points are  and .

Riemann sum is .

.

Substitute corresponding function values in above expression from the graph.

Area under the graph of the function using left endpoints is .

.

(c)

Determine  by Mid points:

Number of subintervals are .

Width of the interval is  :.

Mid points are  and 

Riemann sum is .

, where .

.

Substitute corresponding function values in above expression from the given graph.

Area under the graph of the function using mid points is .

.

(a) Area under the graph of the function using right endpoints is .

(b) Area under the graph of the function using left endpoints is .

(c) Area under the graph of the function using mid points is .