Okay i was busy trying to figure these things out and then i got stuck.

Now using the Riemann notation to calculate the area under the graph

we get the following:

(I calculated

)

They use rectangles under the graph to approximate the area. (6 rectangles and the x-axis value ranges from 0 to 3.)

Then the book goes further and says:

For any number of rectangles under the graph(Still ranging from 0 to 3 on the x-axis):

At the end we arrive at the following:

Up to there i understand perfectly.

Then from that we get