Is every Volterra's function unbounded?

Question

Volterra's function is a function $f\colon\mathbb{R}\to\mathbb{R}$ such that:

• $V$ is differentiable,

• $V'$ is bounded,

• $V'$ is not Riemann-integrable.

http://en.wikipedia.org/wiki/Volterra%27s_function

Is every Volterra's function unbounded?

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I've searched the site and found some results, like

What is an example that a function is differentiable but derivative is not Riemann integrable

Bounded Function Which is Not Riemann Integrable

but is doesn't deal with boundedness of a function.