oh shit you are starting from the beginning

did you attend class the day they did this crap?
its a visual representation of what integration means

integration tells you the area under a graph to the x-axis, positive aread
doing the endpoint thing what they mean is that to calculate the area under a graph physically they break the area into rectangles that have their tops with either the right top corner, left top corner, or midpoint touching the eqaution on the graph
then you use the area of all these little rectangles to estimate the area under the graph
using the 3 different placements of the points give you slightly different answers, and you will see that the more rectangles you use the closer to a perfect answer you get

thus what integration really does is an infinite number of rectangles, giving a perfect slution