@interact
def _(n=int(1)):
if n in ZZ and n>=0:
A=plot(x^2, 0, 1, fill=0)
B=plot(x^2, 0, 1, fill=0)
U=float(0)
L=float(0)
for i in range(n):
A+=plot(0, 0, 1, rgbcolor=(1,0,0))
A+=plot(((i+1)/n)^2, i/n, (i+1)/n, rgbcolor=(1,0,0), fill=0, fillcolor='red')
A+=line([[i/n,0],[i/n,((i+1)/n)^2]], rgbcolor=(1,0,0))
U+=(1/n)*((i+1)/n)^2
B+=plot(0, 0, 1, rgbcolor=(1,0,0))
B+=plot(((i)/n)^2, i/n, (i+1)/n, rgbcolor=(1,0,0), fill=0, fillcolor='red')
B+=line([[i/n,0],[i/n,((i)/n)^2]], rgbcolor=(1,0,0))
L+=(1/n)*((i)/n)^2
A+=line([[1,0],[1,1]], rgbcolor=(1,0,0))
B+=line([[1,0],[1,(1-(1/n))^2]], rgbcolor=(1,0,0))
print "Upper Bound of Area:", U
show(A)
print "Lower Bound of Area:", L
show(B)
else:
print "n must be a non-negative integer."
