Remark 3

The expressions $\int_{x_0}^x f(t) dt$ and $g(t)\Big|_{x_0}^x$ are abbreviating symbols representing assemblies in which the letters $x, x_0, f, g$, but not the letter $t$, appear (cf. Set Theory, I, p. 15); one says that among these symbols $t$ is a "*dummy variable*": one can thus replace $t$ by any other variable distinct from $x, x_0, f$ and $g$ (and from variables which may possibly enter into the proof where these symbols appear) without changing the sense of the symbol so obtained (the reader may compare these symbols with symbols such as $\sum_{i=1}^n x_i$, or $\bigcup X_i$, where $i$ is likewise a dummy variable).