Correct terminology for the joint probability density function?

Question

Suppose I have a joint PDF of two random variables given as: $$f_{X,Y}(x,y).$$ Both of the random variables vary from $0$ to $\infty$. I integrate variable $Y$ to some arbitrary values, i.e., $$f_X(x,0\leq y\leq 5).$$ Now I know that $$f_{X}( x,0\leq y \leq \infty)$$ can be termed as marginal PDF of $X$. But how should I define $f_X(x,0\leq y\leq 5)$? Is it the marginal PDF of $X$ when $Y$ lies in 0 to 5. Does $f_X(x,0\leq y\leq 5)$ qualify to be called as PDF as $$f_X(0\leq x \leq \infty ,0\leq y\leq 5)\neq1$$