The density=True (normed=True for matplotlib < 2.2.0) returns a histogram for which np.sum(pdf * np.diff(bins)) equals 1. If you want the sum of the histogram to be 1 you can use Numpy’s histogram() and normalize the results yourself.
x = np.random.randn(30)
fig, ax = plt.subplots(1,2, figsize=(10,4))
ax[0].hist(x, density=True, color="grey")
hist, bins = np.histogram(x)
ax[1].bar(bins[:-1], hist.astype(np.float32) / hist.sum(), width=(bins[1]-bins[0]), color="grey")
ax[0].set_title('normed=True')
ax[1].set_title('hist = hist / hist.sum()')
Btw: Strange plotting glitch at the first bin of the left plot.