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This lecture covers Riemann sums, a method for approximating the area under a curve by dividing it into multiple subintervals and using the function values at specific points within each subinterval. The instructor explains the concept of Riemann sums, different types of Riemann sums, and how to calculate them for various functions. The lecture also discusses the notation and definitions related to Riemann sums, providing a comprehensive understanding of this fundamental concept in calculus.