Calculus help?

Question

..........π
f(x)=∫(1+cost)dt , f'(x)= ?
..........x

What I am trying to find is the derivative of the integral of (1+cost) from π to x.

Answer 1

Use the fundamental theorem of calculus. Hint: the answer rhymes with f'(x)= -(1+cos(x)).

Answer 2

First, reverse the limits to get -INT[(1+cos t) dt, pi..x]
Now use the fundamental theorem of calculus to
get -(1+cos x).
(Look in your textbook to see why this works.)

Answer 3

the anti derivative is
x-SinT evaluated from 0 - pi