Question: " What are Left and Right Riemann Sum, and How do you solve them? "
Riemann sum is really a approximation of the area under a mathematical curve between two X values.
This area is approximated using rectangles that have a width of Delta X, which is chosen, and a height that is derived from the function f(X) given in the question. The smaller delta X is - the more accurate the approximation will be. The height can be taken from the value of the f(X) either on the right, middle or left of the rectangle.
Just Click on the graphs to the right and you will be taken to the Desmos graph corresponding to the particular type of Riemann sum. change the function, the bounds, and (of course) the number of partition intervals.
Side Note: Georg Friedrich Bernhard Riemann was a German mathematician in the 1800’s who developed mathematics in a number of areas and authored the Riemann Hypothesis, one of the most famous unsolved problems in mathematics.
Riemann 1859: courtesy of the State and University Library at Göttingen