integral in the sense of distributions

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need help for this situation : I have a function real values function $f$ and I have tu study this object : $$ \int_{\mathbb{R}} t \; \mathrm{d}f(t)$$ My function $f$ is decreasing, left-continuous and have a finite number of "jumps". "in the sense of distributions". I don't understand the meaning of "in the sense of distributions".