integral problems?

Question

can some one give me an example of a function f on the intervewl [a,b] with the property that with n = 2 subdivisions.

the integral from a to b of f(x) dx < left hand sum < right hand sum

Answer 1

dx = [b-a]/2

Int [0,10] 2x dx

x^2 [0,2 + x^2 [2,4 + x^2 [4,6 + x^2 [6,8 + x^2 [8,10

=[2^2 - 0^2] + [4^2 - 2^2] + [6^2 - 4^2] + [8^2 - 6^2] + [10^2 - 8^2]
=4 - 0 + 16 - 4 + 36 - 16 + 64 - 36 + 100 - 64
=100 sq units