\int_{c}^{d} (1/u) f(u) du has an upper bound if f(u) is a PDF?

Hi sorry to bother you guys here. I have a question that bugs me quite
a while.

If u \in [a, b], f(u) is a probability density function, i.e, the
integration \int_{a}^{b} f(u) du = 1.
My question is whether the result of the following integration has an
upper bound.

\int_{c}^{d} (1/u) f(u) du, where [c, d] is inside the range of [a, b].


Thanks a lot.
Kun

.

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