Studying hyperbolic partial differential equations, we arrive, in a certain calculation, to the following doubt: every integrable function has a primitive?
If $ u_0 $ is integrable, then $ \exists v_0 $ such that $ \int_b^a v'_0 dt = \int_b^a u_0 dt $?
I think no, but maybe there is some theorem that determines when this holds. And maybe this theorem aplies to our case.
Many thanks for any help!