import numpy as np
import scipy.stats as sts

np.random.seed(123)
y = np.linspace(50,200,150) + np.random.normal(loc=0,scale=15, size=150)
x = np.diff(np.log(y))
mu, sigma = sts.norm.fit(x)
xmin, xmax = x.min(), x.max()
x_l = np.linspace(xmin, xmax, len(x))
dens = sts.norm.pdf(x_l, loc=mu, scale=sigma)
plt.plot(x_l, dens)

dens_kde = sts.gaussian_kde(x)
dens_pdf = dens_kde.evaluate(x_l)
plt.plot(x_l, dens_pdf)

In [152]: from scipy.integrate import simps

In [153]: simps(dens_pdf, x=x_l)
Out[153]: 0.9932706185208222