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In today's lesson, Mr. Bean introduces summation notation and Riemann sums in calculus. By adding multiple Riemann sums, you can find the area under curves accurately. He demonstrates this with examples of one and two sub-intervals, showing how the rectangles approximate the area under the curve from negative one to six. Adding more sub-intervals provides a better approximation of the area under the curve. This concept is essential in calculus for finding precise areas under curves.