How to plot a histogram with unequal widths without computing it from raw data?

Question

Matplotlib's hist says "Compute and draw the histogram of x". I'd like to make a plot without computing anything first. I have the bin widths (unequal), and the total amount in each bin, and I want to plot a frequency-quantity histogram.

For instance, with the data

cm      Frequency
65-75   2
75-80   7
80-90   21
90-105  15
105-110 12

It should make a plot like this:

http://www.gcsemathstutor.com/histograms.php

where the area of the blocks represents the frequency in each class.

Answer 1

Working on the same as David Zwicker:

import numpy as np
import matplotlib.pyplot as plt

freqs = np.array([2, 7, 21, 15, 12])
bins = np.array([65, 75, 80, 90, 105, 110])
widths = bins[1:] - bins[:-1]
heights = freqs.astype(np.float)/widths
    
plt.fill_between(bins.repeat(2)[1:-1], heights.repeat(2), facecolor='steelblue')
plt.show()