How do you estimate the area under a curved graph?

Divide the area under the curve into rectangles (usually of the same width) such that they touch the curve but remain inside it

Find the total area of the rectangles. This area will be less than the required area.

By increasing the number of rectangles, you get a better estimate.

Draw lines at equal widths from the x axis to the curve, Then draw lines between the tops of each of these lines to form trapeziums (you may have a triangle at the start and end if the curve starts and ends on the x axis). Work out the area of each of these shapes and add them together. If the lines at the top are all below the curve you will have an underestimate and if they are above the curve you will have an overestimate of the area.