When we divide the interval from 1 to 5 into 4 subintervals, each has a width of 1. Simpson's rule has us evaluate the integral as
... integral = (1/3)(f(1) +4f(2) +2f(3) +4f(4) +f(5)) = (1/3)(10 +4·25 +2·46 +4·73 +106)
... integral = (1/3)(600) = 200 . . . . . by Simpson's rule
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The integral evaluates to
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Simpson's rule uses a quadratic interpolation, so evaluates quadratics exactly.