My teacher said that the equation v(t) for Vcap (in image) will be V = -1/C integral of i(t) + v(initial). My question is, my teacher has said that the '-' infront of the 1/C is because the current flows into the negative terminal of the capacitor. But in the answer my teacher has put v(initial) as +20 and not -20, even though the 20V across the capacitor is also negative to positive as shown in the image. So why is the v(initial) put as +20 and not -20? Thank you.

My teacher said that the equation v(t) for Vcap (in image) will be V = -1/C integral of i(t) + v(initial). My question is, my teacher has said that the '-' infront of the 1/C is because the current flows into the negative terminal of the capacitor. But in the answer my teacher has put v(initial) as +20 and not -20, even though the 20V across the capacitor is also negative to positive as shown in the image. So why is the v(initial) put as +20 and not -20? Thank you.