Best way to write a Python function that integrates a gaussian

def make_gauss(N, sigma, mu):
    return (lambda x: N/(sigma * (2*numpy.pi)**.5) *
            numpy.e ** (-(x-mu)**2/(2 * sigma**2)))

quad(make_gauss(N=10, sigma=2, mu=0), -inf, inf)

quad(gen_gauss, -inf, inf, (10,2,0))

def make_gauss(N, sigma, mu):
    k = N / (sigma * math.sqrt(2*math.pi))
    s = -1.0 / (2 * sigma * sigma)
    def f(x):
        return k * math.exp(s * (x - mu)*(x - mu))
return f

import scipy.special
help(scipy.special.erf)

from scipy.integrate import quad
from math import pi, exp
mean = 0
sd   = 1
quad(lambda x: 1 / ( sd * ( 2 * pi ) ** 0.5 ) * exp( x ** 2 / (-2 * sd ** 2) ), 0, inf )