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**: is like the x-coordinate values, also gives the number of times the graph was chopped up. We need them in order to find the distance or length of each rectangle. The distance is found by taking the further point minus the point prior to it. The partition is usually written like P = {0,1,2,3,4}**

*Partition***: would be each of the x-coordinates but broken into a series of intervals like: (0,1),(1,2),(2,3),(3,4) not sure exactly why this is needed. Maybe to get distance easier?**

*Sub-intervals***: is when you take the lowest values between each subinterval and then take that value and plug it into the original function. You then multiply that function with distance between the subinterval and consecutively add them all together and the result gives the total Area.**

*Lower value***: same process for lower value except you take the highest value in the subinterval.**

*Upper value***same process for lower/upper sum but with the stipulation of taking the right-most point.**

*Right-hand sum:***: same process but for the left-most point.**

*Left-hand sum*__: (b-a)/n, I don't know what that means. I think it has something with taking a subinterval then subtracting the upper value with the lower value and that generates the midpoint? not sure, then the process would still hold true for the others just don't know how to get the midpoint initially.__

*Midpoint sum*Please correct any mistakes or inconsistiencies

Thank you!