From Förberedande kurs i matematik 2

The notation \displaystyle \int{\sin x\,dx} is called the indefinite integral of \displaystyle \sin x and means all primitive functions of \displaystyle \sin x.

Because \displaystyle \sin x is a standard function, we know from the course notes that its primitive functions are

\displaystyle \int{\sin x\,dx}=-\cos x+C

where \displaystyle C is an arbitrary constant.