Integral of greatest integer function.

Question

$[x]$ denotes the greatest integer $\leq x$. Let $f(x)=[x]$

What is the indefinite integral (without limits) of $f(x)$ ?

And if $f(x) = e^{-7[x]}$ what would the indefinite integral be?

Answer 1

$\int[x]~dx=x[x]-\dfrac{[x]([x]+1)}{2}+C$