The shown below amount of property damage (in dollars) due to automobile accidents in California in recent years. In this exercise we are interested in the total amount of property damage due to automobile accidents over the 8-year period from mid-2009 to mid-2017 using the data for the 9 years.

(a) One approach is to sum up the numbers in the second column, but count only half of the first and last numbers. Give the answer to this calculation.
(b) Approximate the amount of property damage over the 8-year period 2009–2017 by taking the average of the left endpoint sum and the right endpoint sum. Explain why this is equivalent to the calculation done in part (a).

(c) Find the equation of the least squares line for this data, letting t = 0 correspond to 2000. Then integrate this equation over the interval 39, 174 to estimate the amount of property damage over this time period. Compare with your answer to part (a).

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Year Property Damage ($) 2009 2010 2011 2012 2013 2014 2015 2016 2017 259,889 252,876 241,886 233,447 224,078 233,941 256,104 292,672 289,279