anti-derivative not differentiable at any point Reading about primitives and anti-derivatives, I noticed that primitive functions of non-continuous functions are not differentiable at some point, but the set of non-differentiability is often negligible.
I tried to think of a function horrible enough to  get a non-differentiable antiderivative, and I found some with non-negligible set of non-differentiability points.
But I never found an antiderivative that is nowhere differentiable. 
Can you find one?

It isn't possible. Lebesgue's Differentiation Theorem states that if $f$ is integrable over $\mathbb{R}$, and we let:
$$
F(x) =
\int \limits_{(-\infty, x]} f(t) \, dt
$$
Then $F$ is almost everywhere differentiable.
