$\displaystyle F(x)+5=\int_{2}^{x}sin(\frac{\pi t}{4})dt$

what is $\displaystyle F'(2)+F(2)$

-my steps

$\displaystyle F'(x)=sin(\frac{\pi 2}{4}) - 5=sin(\frac{\pi }{2})-5=1-5=-4$

then i realized something...

since a derivative and an integral are inverses. Isn't F'(x)+F(x) always gonna equal 0?

I am right or going crazy?

All thanks is appreciated.