I've always assumed by graphical inspection that
$\int (x - \lfloor x\rfloor)\mathrm dx = \dfrac{(x - \lfloor x\rfloor)^2 + \lfloor x\rfloor}{2}$ (W|A) and
$\int \lfloor x\rfloor\mathrm dx = x\lfloor x\rfloor - \dfrac{\lfloor x\rfloor(\lfloor x\rfloor + 1)}{2}$ (W|A)
Why does Wolfram|Alpha say for each integral, "no result found in terms of standard mathematical functions"?
I also assumed that $\frac{\mathrm d}{\mathrm dx} \lfloor x \rfloor = 0$, yet according to Wolfram|Alpha $\frac{\mathrm d}{\mathrm dx} \lfloor x \rfloor = \mathop {\rm floor}'(x)$—which is not not explained, but the graph looks very strange. What is going on here?