Integration paradox

Question

Yesterday i was doing a question where when you integrate Sinx dx from 0 to 90 degree you get -1+c as answer and for 90 to 180 you get 1+c as answer and when integrate it for 0 to pi you have 2 as answer but when add up individual integrated answer sum would be zero since c=0 cuz there is no vertical shift.

Answer 1

Remarks: you should not have $c$ (arbitrary constant) when you deal with definite integral.

Also potential mistake in your first integral: $$\int_{0^\circ}^{90 ^\circ} \sin x dx = [-\cos x]|_{0^\circ}^{90^\circ}=0-(-1)=1$$