AP Calculus allows you to bring a graphing calculator, and one of the approved calculator was the TI Nspire CAS, which has a very sophisticated computer algebra

AP Calculus allows you to bring a graphing calculator, and one of the approved calculator was the TI Nspire CAS, which has a very sophisticated computer algebra system that can do a lot of the things wolfram alpha can - like calculating the antiderivative. So you might be overestimating how much advantage wolfram alpha can confer :)