How to Integrate 1-cos(t)dt and Prove the Resulting Derivative

[bocobuff]

Homework Statement

it's been a long summer and i forgot everything.
i need help integrating 1-cos(t)dt

evaluate g(x) = [\pi,x]integral (1-cos(t))dt

i know by pt2 of fund. thm of calc that g' (x) = 1-cos(x)
but i can't remember how to evaluate the integral and then differentiate to prove my answer.\
I should just know the integral of 1-cosx but I'm retarded and forgot what to do.
any help?

 

[jeffreydk]

Well you know that by the properties of integrals, you can treat it as two integrals
I=I_1+I_2=\left(\int 1dt\right)+\left(-\int\cos{t}dt\right)
Do you know these integrals? What is the derivative of -\sin{t}?