![enter image description here](https://i.stack.imgur.com/S5Pth.jpg)

Hello. 
I inserted an image because it's easier to understand my questions. 

I don't understand how pdf works. If I say I want te probability of X=1, it returns me 0,667. But what's that? Is it the whole area under the triangle of base 1 and height 0,667? So why doesn't A=b\*h/2 equal to 0,667? A=2/6=1/3 ;

Also, if I do the integral of the function (2/3)\*x shouldn't it give me the same result as f(1) = 2/3 ? Since the fdp says that the area below the graph is the probability of X=k.. 

Lets say my random variable is the kilograms of rice that people buy in a store. The probability o X=1 kilogram is zero, because the area under the graph is zero. So it makes more sense to say we want P(0