#!/usr/bin/python
from matplotlib import *
from pylab import *

a=1
b=5
n=8
h=1.0*(b-a)/n
def f(x):
    return x**2

x=[a+i*h for i in range(n)]
y=[f(a+i*h) for i in range(n)]
areas=[f(a+i*h)*h for i in range(n)]
area=sum(areas)

print "x=",x
print "y=",y
print "areas=",areas
print "area=",area

plot(x,y,color='red')

for i in range(n):
    matplotlib.pyplot.gca().add_patch(matplotlib.patches.Rectangle((a+i*h,0),h,f(a+i*h)))

show()