Yes, but it times out rather quickly. Mathematica is much more powerful.

(For those interested: the relevant syntax is

    Integrate[x^2, x]

or

    Integrate[x^2, {x, 0, 1}]

You can find more Mathematica at http://reference.wolfram.com/mathematica/guide/Mathematica.h...; searching the Mathematica docs is often easier than figuring out which textual query Wolfram|Alpha understands.)

No not always. I've tried several times, but W|A pipes the input first trough the natural language processor. http://www.wolframalpha.com/input/?i=DateListPlot[++WeatherD...]