Hello, sorry I can't really use the math function well yet I need to learn it

My question is about this:

Integral (1/t^2)cos(1/t - 1)dt

I substituted with u = 1/t - 1 and du = 1/t^2

For a final answer I get cos(1/t - 1) + c but the book says it's

-sin(1/t - 1) + c.

I don't see when the cosine was derived?..