title: How to shade region under the curve in matplotlib
body: <p>I want to use matplotlib to illustrate the definite integral between two regions: x_0, and x_1. </p>
  
  <p>How can I shade a region under a curve in matplotlib from x=-1, to x=1 given the following plot</p>
  
  <pre><code>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))
  </code></pre>