nclude your answers, full explanation and justification, and context for your answers $($including

units$),$ as appropriate. The more we have to guess about what you were thinking, the less credit

you will receive

Problem $2.$ Darnell goes out for a "run." His wife rides behind him on a bicycle and clocks

his speed every few minutes. He starts out strong for an old guy, but after $30$ minutes he stops

after remembering he really doesn't like running. He gets an Uber home for a snack and a nap.

Give an upper and lower estimate for the distance Darnell ran in total during the $30$ minutes.

Explain the reasoning behind your estimates, using the principles of calculus.