Use Geogebra (Free download: to open this file and see the effect of increasing the no. of rectangles 'n'.

(Download the offline installer, not the webstart, which is not as good.)

-You should see a straight line graph, f(x) = x. Move the slider to see the effect of increasing 'n'
-Click on View --> Algebra View to open the panel on the left. You can click on f(x) = x and change it to f(x) = x^2 to see the curve f(x) = x^2 instead.

The main idea is to know that as you increase the no. of rectangles, the total area of the rectangles will become the area under the curve as n tend towards infinity.

That is the idea of how Integration is derived to find area under curve.

Note: Area under curve is not quite the correct term. It is used out of convenience. It should be "Area bounded by the curve, x-axis and the lines x = a and x = b". If the area is above the x-axis, it will be a positive value, if it's underneath the x-axis, it will be negative, in which case you just need to take its absolute value (Modulus).

For SMTP (2015 onwards), Volume of revolution is included in the syllabus