Can somebody please explain , in simple terms , if continuity ALWAYS imply integrability ? If it doesn't ? Maybe some counter examples?
Or maybe even what are the necessary conditions in order to imply that a continuous function can be integrable?
Moreover, i wanted to be sure that differentiabilility always implies continuity ... is this correct? I mean if i say that f is differentiable on point a then f is continuous on point a . is that wrong to say ? Or may it be right to say that if a left and right derivative of a fucntion exist at a point a , then there exists the left and right continuity at point a. Left and right continuity at point a together imply continuity .