Suppose the temperature for thus Saturday can be modeled by f(x) = 75 + 10 sin ((π/12)x), where x is the number of hours past 9 am. You are training for a marathon and have to complete a run on saturday that will take you 2 hours. Due to other committments on Saturday, you only have the options to for time to complete your run: 8am to 10am, 12pm to 2pm, or 7pm to 9pm. Set up and evaluate three definite integrals to determine which of these three options will result in the lowest average temperature for your run.