How to find + c without given information

[XTTX]

OK, well this is probably a pretty basic problem. I understand all of it except for one part.

Homework Statement

If $$F(x)=\int^{x}_{0} sin(t)dt$$, where x $$\geq$$ 0, what is the maximum value of F?

Homework Equations

$$F(x)=\int^{x}_{0} sin(t)dt$$

The Attempt at a Solution

$$F(x)=\int^{x}_{0} sin(t)dt = -cos(x) + c$$
max = 1 + c

How do you find c?

If solving with a graphing calculator: $$y^{}_{1} = Fnint(sin(t),t,0,x)$$ then the answer is 2; I just don't know how the calculator found the shift.

 

[Tedjn]

Actually, the C should not be there, because you have a definite integral That is, your solution F(x) is actually [-cos(x) + C] - [-cos(0) + C], and the C cancels out.

 

[XTTX]

Oh wow, I feel really dumb now XD. I guess pulling an all-nighter isn't the best thing for my brain, but thank you for clearing that up.