Consider the Dirichlet function: f(x) = 0 if x is rational, 1 otherwise
This function has no derivatives, so integral(derivative) does not exist.
However, I believe its Lebesque integral is x (plus a constant). The derivative of its integral = 1, which is not the same as f(x).
So, f(x), the derivative of the integral and the integral of the derivative can all be different.
Of course, this problem is only difficulty = 1, so I expect that this is not the expected answer.