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all right everybody lets take a look at some riemann sums okay so again pause as you need to to take the notes and uh to go through the examples at a good pace for yourself all right so riemann sums um as the note say here is using rectangles to approximate the integral value of a function on the closed interval a b okay so integral value okay bounded integrals is what were going to be talking about here and thats going to refer to the area between the graph of f and the x-axis on the integral a b okay so the integral from a to b of f of x dx thats how we notate that represents the area between f and the x-axis on the interval okay so again you know we saw with upper and lower sums using rectangles to approximate these areas okay well riemann sums again does that it uses rectangles to approximate the integral value or area between the function and the x-axis on the closed interval a b so we have seen upper and lower sums there are three other riemann sums left right and midpoint su