Your table doesn't look right? If the function is 1/(1+ x^2) then should f(1) = 1/2 , f(2) = 1/5 ... etc. You got some weird numbers
The height is right, but you applied Simpson's rule wrong. The correct form is
h/3 ( f(x1) + 4f(x2) + 2f(x3) + 4f(x4) + 2f(x5) + ... f(xn))
i.e. it alternates between 4's and 2's as the coefficients, you only took the 4's.