I am supposed to give reasons why function P is a primitive function. I have to explain it as a general method for determination of area or volume of geometric figures.
What I have so far:
Function f is nonnegative function, which is continous on interval [a,b]. For every $$ t \epsilon [a,b]$$ we label P(t) as area of figure given by these conditions: $$ \left \{ [x, y]; a\leq x\leq t, 0\leq y\leq f(x) \right \} $$ For h>0 we have: P(t+h)-P(t) is area of figure given by: $$ \left \{ [x, y]; t\leq x\leq t+h, 0\leq y\leq f(x) \right \} $$ And now I know that I have to use continuity of function together with $$ \varepsilon ,\delta $$ and make a conclusion.
This is the description with the picture. But I am not sure if I get it right, or I think that I understand the explanation of the picture, but I have a feeling that I do not understand the whole idea behind it.
Can anyone please describe it?