Not exactly a question about distributions as it is about approximating the area under the curve using rectangles.
The (horizontal) length of each rectangle is the difference between successive values of [tex]x[/tex]. For example, in the first rectangle, the length is starting at [tex]x_0=650[/tex] and terminates at [tex]x_1=675[/tex], giving a difference of [tex]\Delta x=x_1-x_0=25[/tex].
The (vertical) height of each rectangle is the value of the function [tex]f(x)[/tex] taken at the point [tex]x[/tex] that gives the left endpoint of the rectangle's width. So in the first rectangle, you take [tex]f(650)[/tex].
Then the area of each rectangle is simply the length multiplied by the height.
Area of 1st rectangle = [tex](675-650)\times f(650)=25\times0.001295=0.032375[/tex]
2nd = [tex](700-675)\times f(675)=25\times0.000863=0.021575[/tex]
3rd = [tex](725-700)\times f(700)=25\times0.00054=0.0135[/tex]
and so on.
The total area would then be the sum of all the rectangles' areas.
