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- Use the Riemann sum midpoint rule to calculate the distance John run in 5 secondsTea leaves are placed in a cup of hot water. Caffeine is infused into the water at a rate of 15 −(x3/14) milligrams per minute. After 6 minutes, the tea leaves are removed. a) Estimate the amount of caffeine in the cup of water after the tea leaves are removed using a right Riemann sum with 3 subintervals.