from matplotlib.pyplot import *
 from numpy import *
 from scipy.integrate import cumtrapz

 def f(x):
     return x*sin(1/x)

 eps = 1e-9
 x0 = linspace(0, 1-eps, 100)
 x1 = linspace(1, 2-eps, 100)
 x2 = linspace(2, 3-eps, 100)

 int_x0 = x0-modf(x0)[1]
 int_x1 = x1-modf(x1)[1]
 int_x2 = x2-modf(x2)[1]

 x = hstack((x0, x1))
 int_x = hstack((int_x0, int_x1))

 first_prim = cumtrapz(int_x, x, initial=0)
 second_prim = cumtrapz(first_prim, x, initial=0)

 plot(x0, int_x0, color='blue', lw=2)
 plot(x1, int_x1, color='blue', label=r'$f(x)=x-\lfloor x \rfloor$', lw=2)

 plot(x, first_prim, color='red', label=r'$F(x)=\int_0^x f(t)dt$', lw=2)

 plot(x, second_prim, color='green', label=r'$\int_0^x F(t)dt$', lw=2)

 legend(loc=2)
 tight_layout()
 show()