Maclaurin Series and Term by Term Integration

Hey :)

"Suppose the interval of convergence of the Maclaurin series for f(x) is -2<x<2. If the Maclaurin series for the integral of f(t) dt from 0 to x is obtained by integrating term by term, which of the following could be the interval of convergence of the new series? Justify.

I. -2<x<2

II. -2<= x < 2

III. -2 < x <= 2

IV. -2 <= x <= 2

It can be more than one.

Thanks for your help

Re: Maclaurin Series and Term by Term Integration

I would say all, because it depends on your the series you are interested in. If you give a particular series there are tests that can be used to determine which possibility it would be. (It's only all of them because of the word "could" within the question.)

P.S. I might be wrong. =P

P.P.S. But I think I'm right.