Suppose routine integration by parts yields:

$\displaystyle \int f(x)\,dx = g(x) + \int h(x)\,dx + C$

Where $\displaystyle h$ does not necessarily have an antiderivate.

Then is it correct to assume that $\displaystyle \int_a^b f(x)\,dx = g(b)-g(a) + \int_a^bh(x)\,dx$?

Thanks for any help.

James