Integration tells you the area under a curve. How similar are your results? Substitute in those limits - the results should be very similar.
I am working on a question where I am given (1 + x^2)^5 and asked to expand out (using binomial expansion). I have no problem with that.
Then I am asked to integrate the equation for values 0 -> 0.4. No problem there.
But then it asks how the estimation of the area using the binomial expansion compares with the integration result? What is that about?