Mentally integrate first.  Will you get an expression or just a constant?  What happens when you take the derivative next to the constant?

Product Rule or Quotient Rule, depending how you write $t^{ −1}$.

Refer to the hint in part (a). But notice that this is an integral of a derivative, not the reverse. That means that this answer will include $+C$.

Both parts of the sum in the integrand have antiderivatives that are trig (or inverse trig) functions.