Find the antiderivative Fx and fx that satisfies the given c

Find the antiderivative F(x) and f(x) that satisfies the given condition. using the constant C for the antiderivative find out what C is. Please show your work. thank you. f(t) = cos t + sin t

F(?) = 1

?

Solution

F(x) = integral of f(x) = sinx - cosx +C given F(0) =1 =>C=2 =>F(x) = sinx - cosx +2