Numerical integration in 1D: for a given function f:R→R and an interval (a,b)⊂R, compute an approximation of ∫ f(x) dx using

• the rectangle rule,
• trapezoidal rule,
• Keplersche Fassregel (barrel rule).
• Emphasize the connection to Lagrange polynomials (Hint: see Newton-Cotes formulas).