# Construct the linear spline ``x if x < 1 else 2 - x`` on the base
# interval :math:`[0, 2]`, and integrate it

from scipy.interpolate import BSpline
b = BSpline.basis_element([0, 1, 2])
b.integrate(0, 1)
# array(0.5)

# If the integration limits are outside of the base interval, the result
# is controlled by the `extrapolate` parameter

b.integrate(-1, 1)
# array(0.0)
b.integrate(-1, 1, extrapolate=False)
# array(0.5)

import matplotlib.pyplot as plt
fig, ax = plt.subplots()
ax.grid(True)
ax.axvline(0, c='r', lw=5, alpha=0.5)  # base interval
ax.axvline(2, c='r', lw=5, alpha=0.5)
xx = [-1, 1, 2]
ax.plot(xx, b(xx))
plt.show()