Suppose a function is defined as $I(x) = \int_{0}^{x}g(u)du.$ Does there exist constant bounds of integration $I(c)$ such that $I(x) - I(c) = \int_{0}^{x-a} g(u)du.$ Or in other words, is it possible to lag the boundary of $I(x)$ by some constant using non-variable bounds of $g(u)$? I suspect not but I don't know for sure.
Would this change for the infinite case $I(x) = \int_{-\infty}^{x}g(u)du$ to subtract some other bound, either $\int_{a}^{b}g(u)du$ or $\int_{-\infty}^{c}g(u)du$ where $a, b, c$ are contants?
Another way of phrasing this:
Can $\int_{b}^{x-a}g(u)du$ be decomposed into some $\int_{b}^{x-a}g(u)du = \int_{b}^{x}g(u)du - \int_{c}^{a}g(u)du$, where $a$ and $b$ and $c$ are constants?
