Hi, colleagues!

On calculus books I read the following formula about the solution of definite integrals by parts:

http://img83.imageshack.us/my.php?im...9234525cz4.jpg

where f, g : [a,b] c R -> R , derivatives of F(x), G(x), are continuous in [a,b].

So, why I can't solve

with g(x) = sin(x), F(x) = 1/cos(x), a= pi/4, b= pi/3

even if f,g are continuous in [pi/4, pi/3] ?