Rectangular Approximation: Finding the area under the curve utilizing a given amount of rectangles, then choosing the points on those rectangle corners (left or right) that touch the curve. The more rectangles, the more accurate the approximation.
Riemann sums: Finding the area under the curve using an INFINITE amount of rectangles– therefore most accurate (note: a more efficient way of doing this will be introduced with integrals, however, this is still vital to learn in our curriculum)
Riemann Sums and Rectangular Approximation (cr: The Organic Chemistry Tutor)
Your calculus book also discusses the Trapezoidal rule which is useful however, you will probably not be tested on (still fun to do!) (cr: The Organic Chemistry Tutor)