Find the approximate area under the curve by dividing the intervals into n subintervals and then adding up the areas of

[answerhappygod]

Find the approximate area under the curve by dividing the intervals into n subintervals and then adding up the areas of the inscribed rectangles. The height of each rectangle may be found by evaluating the function for each value of x.
n1 = 12
n2 = 5
​ between x = 0 and x = 6 for n1 and n2
Find the exact area under the curve using integration ​between x = 0 and x = 6
Please explain the reason for the difference in the answers
Please show step by step so I can understand it.
Thank you