You are sitting on the bank of a tidal river watching the incoming tide carry a bottle upstream. You record the velocity of the flow every 5 minutes for an hour, with the results shown in the accompanying table. About how far upstream did the bottle travel during that hour? Find an estimate using 12 subintervals of length 5 with

a. Left-endpoint values.

b. Right-endpoint values.

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Time Velocity (min) (m/sec) 0 5 10 15 20 25 30 1 1.2 1.7 2.0 1.8 1.6 1.4 Time (min) 35 40 45 50 55 60 Velocity (m/sec) 288220 1.2 1.0 1.8 1.5 1.2