python - How to shade region under the curve in matplotlib

Question

I want to use matplotlib to illustrate the definite integral between two regions: x_0, and x_1.

How can I shade a region under a curve in matplotlib from x=-1, to x=1 given the following plot

import numpy as np
from matplotlib import pyplot as plt
def f(t):
    return t * t

t = np.arange(-4,4,1/40.)
plt.plot(t,f(t))

Answer 1

The final answer I came up with is to use fill_between.

I thought there would have been a simple shade between type method, but this does exactly what I want.

section = np.arange(-1, 1, 1/20.)
plt.fill_between(section,f(section))