Why does negative indefinite integral sinxdx turn into posit

Why does negative indefinite integral sinxdx turn into positive cosx....I understand that anti derivative of -sinx = positive cosx...but i didnt think that mattered if the negative was pulled out in front and then just anti derive what is inside the integral leaving the negative alone??Am i wrong that even if the -1 is pulled out in front of the integral that you must treat it as it is a negative...SHould I leave the -1 inside and just say it is +sinx????Thank You

Solution

if you take out -1 outside you will be left with integration of sin x .. integration of sin x = - cosx so we get -1*-cos x = cos x hence the result
Why does negative indefinite integral sinxdx turn into positive cosx....I understand that anti derivative of -sinx = positive cosx...but i didnt think that matt

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