I have a question on limits of integration. The exercise is as follows:
Give an example of a step function f, defined on the closed interval [0,5], which has the following properties:
$$\int_0^2 f(x) \,dx= 5$$ $$\int_0^5 f(x) \,dx= 2$$
One solution is given as:
$$f(x) = \frac52$$ if $$0 <= x < 2$$
and
$$f(x) = -1$$ if $$2 <= x <= 5$$
My question is: Would the following answer also be true?
$$f(x) = \frac52$$ if $$0 <= x <= 2$$
and
$$f(x) = -1$$ if $$2 < x <= 5$$