I have been asked to justify if the following statement is true or false.

'If the integral of f(x) >= 0 on [a,b], then f(x) is >= 0 on [a,b].

Would (8-x^2) over the domain [-4,4] be a counter example to this? thus justifying that the statement is false.

I beleive so as f(x) is <= 0 for some values but the area over that domain is positive. Can anyone tell me if iam on the right path?