I was going through my textbook today and I found this question which defined a function $f(x)$ as $$f(x)=\int_0^{x}\sin{(\lfloor{2x}\rfloor)}dx$$
and was asking to calculate $f(\frac{\pi}{2})$.
I get that the question wants me to evaluate,
$$f(x)=\int_0^{\frac{\pi}{2}}\sin{(\lfloor{2x}\rfloor)}dx$$
But this notation is bothering me because of the $x$ inside the integral. Shouldn't the proper notation be, $$f(x)=\int_0^{x}\sin{(\lfloor{2t}\rfloor)}dt$$
Am I wrong?
Thanks for the help.