Hey MarcLeclair.

Can you show us youatr working for 1?

For 2) Yes you need to use FTC but remember that you have a 1 + sin(x) and not an x so you will need to use the chain rule.

For 3) try considering that you have a function given by the integral and to find a maximum, you find when the derivative of that function is 0 with 2nd derivative being less than zero.