Show me how this equation is valid

[oahz]

Please, hurry. It's driving me nuts

 

[economicsnerd]

I suppose $f \geq 0$? If so, $y\geq x \implies yf(y) \geq xf(y)$.

 

[Nick O]

Seconded. Note that y takes on every value >= x, so you have basically replaced the constant x with the increasing function y in the integral.