Explore numerical integration techniques for approximating definite integrals and finding the area under a curve in this 30-minute video lecture. Delve into approximations of the Riemann integral, including left and right rectangle rules, trapezoidal integration, and Simpson's rule based on spline interpolation. Examine the error of each method, learn how to implement them in Python and Matlab, and understand their relationship to other intuitive numerical schemes. Benefit from visual explanations and practical code examples to reinforce your understanding of discrete numerical methods for integration.