I was wondering about the integration of -1/sqrt(1-x^2) with respect to x. The integral of 1/sqrt(1-x^2) is inverse sin(x)+c, but the integral of -1/sqrt(1-x^2) is inverse cos(x)+c. However, surely according to the rules of integrals you can write the integral of -1/sqrt(1-x^2) as -1*integral of 1/sqrt(1-x^2), i.e. -1*inverse sin(x)+c, which is obviously different from inverse cos(x)+c. I was wondering how these two integrals of the same function are the same. Sorry if it's a stupid question. Thanks.