You can't have one that can do algebraic integration (ie. indefinite integrals) but you can have one that can do numerical integration (definite integrals). They might not check, but they may well do. Some schools will have your class teachers invigilating and it really isn't worth getting a zero for the sake of an extra mark or two that it might help you. They also cannot do anything algebraic (solving equations. Graphical are fine.
In my experience, confused invigilators will often confiscate calculators that are not the standard Casio, which is frustrating, especially the bigger TI-84 type ones, even if they aren't graphical calculators. I would stick to one the two Casio ones (either than standard one or the 99ES integration one) and avoid risk. TI-89 and TI-92 are generally banned.