Integration by parts when only the definite integral is known

I have

$$\int\limits_a^b v' dx = A$$

$$\int u'dx = u$$

That is I have the definite integral of $v'$ and the indefinite integral of $u'$. $v$ is unknown.

I want to evaluate by integration by parts:

$$\int\limits_a^b u v'dx = ?$$

• This will not be possible in general. Oct 20 '16 at 21:01