Am I using the Simpsons rule and Gauss-Legendre method correctly?

Question

I have the integral here:

Simpsons rule: Answer 414.11411

Gauss-Legendre method

Here the limits are x+y I found the answer to be around 0.923

Just wanted to make sure these values are correct.

Answer 1

Using $\Gamma=2$, the exact value is

$$\int_{-2}^2\frac{dm}{m^2+1}=2\arctan 2=2.2142974355881810060341309203571\cdots$$

A few values by the Gauss-Legendre method:

$$n=2\to1.714285714$$ $$n=3\to2.431372549$$ $$n=10\to2.214043446$$ $$n=20\to2.214297419$$

Don't forget the scaling factor.