How can i integrate cost without using substitution?

So the question ask to find how to integrate cos2t without using substitution and base on my research, the integral of the cos2t  = (1/2) sin(2t), and negate the said integral because the derivative of cosx is - sinx. I hope you are satisfied with my answer and feel free to ask for more 

10,000 hope i ! : )

C, e, and a (hope it )