When estimating the area under a curve, you need to split the area under the curve into a number of distinct shapes; the total area of those shapes will give you an estimate of the area under the curve.

Obviously this method will not give you an accurate result, so what you need to also determine is whether your answer is an over-estimate or an under-estimate.

Example 1

Example 2

Congruent vs Similar Shapes
Scatter Diagrams