The table lists several measurements gathered in an experiment to approximate an unknown continuous function y = f (x).

(a) Approximate the integral ∫²₀ f(x) dx using the Trapezoidal Rule and Simpson’s Rule.(b) Use a graphing utility to find a model of the form y = ax³ + bx² + cx + d for the data. Integrate the resulting polynomial over [0, 2] and compare the result with the integral from part (a).

x 0.00 y x y 4.32 1.25 7.25 0.25 0.50 4.36 4.58 1.50 7.64 0.75 5.79 1.75 2.00 8.08 8.14 1.00 6.14