Can someone intuitively explain why it is that $$P(X>x)=\int\_x^{\infty}f\_X(y) \ dy?$$

I don't see how i can enterpret the integral as an area. Area of what? what is $f\_X(y)$ in this case? why integrating w.r.t $y$ if we have a function of $x$ in the left side? If we multiply both sides by $-1$ we get

$$-(1-P(X<x))=-1+F\_X(x)=\int\_\infty^xf\_X(y) \ dy,$$

but this does not make any sense :S.