1"""
2==================================
3Integral as the area under a curve
4==================================
5
6Although this is a simple example, it demonstrates some important tweaks:
7
8* A simple line plot with custom color and line width.
9* A shaded region created using a Polygon patch.
10* A text label with mathtext rendering.
11* figtext calls to label the x- and y-axes.
12* Use of axis spines to hide the top and right spines.
13* Custom tick placement and labels.
14"""
15import numpy as np
16import matplotlib.pyplot as plt
17from matplotlib.patches import Polygon
18
19
20def func(x):
21    return (x - 3) * (x - 5) * (x - 7) + 85
22
23
24a, b = 2, 9  # integral limits
25x = np.linspace(0, 10)
26y = func(x)
27
28fig, ax = plt.subplots()
29ax.plot(x, y, 'r', linewidth=2)
30ax.set_ylim(bottom=0)
31
32# Make the shaded region
33ix = np.linspace(a, b)
34iy = func(ix)
35verts = [(a, 0), *zip(ix, iy), (b, 0)]
36poly = Polygon(verts, facecolor='0.9', edgecolor='0.5')
37ax.add_patch(poly)
38
39ax.text(0.5 * (a + b), 30, r"$\int_a^b f(x)\mathrm{d}x$",
40        horizontalalignment='center', fontsize=20)
41
42fig.text(0.9, 0.05, '$x$')
43fig.text(0.1, 0.9, '$y$')
44
45ax.spines.right.set_visible(False)
46ax.spines.top.set_visible(False)
47ax.xaxis.set_ticks_position('bottom')
48
49ax.set_xticks((a, b))
50ax.set_xticklabels(('$a$', '$b$'))
51ax.set_yticks([])
52
53plt.show()
54