2.2 Explore the numerical integration of the function f(x) = x² + 2x + 3 using methods for approximating definite integrals. a. Calculate the definite integral of f(x) over the interval [a,b] using the Trapezoidal Rule, where a and b are specified values. b. Estimate the definite integral of f(x) over the same interval [a,b] using Simpson's Rule. c. Compare and contrast the results obtained from the Trapezoidal Rule and Simpson's Rule for the specified interval [a,b]. Discuss the accuracy, efficiency, and computational requirements of each method. d. Explain the significance of numerical integration techniques, such as the Trapezoidal Rule and Simpson's Rule, in solving real-world problems where analytical solutions are impractical. Discuss their role in approximating the area under curves.