Improper integrals Memes

Left side: A sophisticated mathematical expression with a monocle exclaiming "Oh, my word!" - that's your proper integral with well-defined bounds. Right side: The wild, unbounded integral screaming "YELL YEAH!!!" like it just escaped from calculus prison. Math nerds know the struggle. One gives you a nice, civilized answer; the other might diverge to infinity and crash your homework. It's basically the difference between inviting calculus to a tea party versus finding it doing keg stands at 2am.