The problem is we cannot find anti-derivatives on closed intervals, we require that in that case and hence the anti-derivative is on and a constant everywhere.
So,
But needs to be continous differenciable at as well. So and where is any arbitraty konstant.
Well I still don't like it so I will do the following instead:
Then:
and if you add an arbitary constant onto this you will still have an anti-derivative of .
If everything has worked out right with the extra arbitary constant this should be the same as the soution given by ImPerfectHacker.
RonL