(No program is required for this problem.) Simpson's rule for numerical integration [f(x)dx] approximates a function f(x) (blue curve in the figure) by a parabola, f(x) = ax + Bx+y, within two consecutive intervals. Assume that the x-interval, 1x1, is divided by N=3 points only: x= 1, x2=0, and x3=1. For these points the values of the function are, f(1)=2.1, f(0)=4.5, and f(1)=0.8. Show that there is one and only one parabola (red, dashed) associated with the 3 points of f(x) -1.0 -0.5 0.0 0.5 1.0 x the function and find its coefficients, , B, and y. Using Simpson's rule with N=3 points, solve the 1 integral f(x)dx of this function. -1