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.
But needs to be continous differenciable at as well. So and where is any arbitraty konstant.
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.