Simpson's method for numerically computing the integration of a function
There is no reason to allocate the double[] x array. It is better to compute the argument as you go: initialize double x = a; and increment it x += delta_x; in the loop body.
if in the loop is usually a performance killer. Consider incrementing j by 2:

    for (int j = 1; j &lt; n; j += 2)
    {
        sum += 2 * Function(x);
        x += delta_x;
        sum += 4 * Function(x);
        x += delta_x;
    }


Now depending on the parity of n the very last addition could be wrong, and you need to compensate for it.
Function shall not be a Simpson's method. The Simpson shall not care what it integrates. Change the signature of Compute to accept the callable.
The choice of \$\dfrac{1}{1 + x^5}\$ for an integrand looks strange. It is hard to verify that the result is correct. I recommend to test against some more friendly integrands first.