You examples are easy, I was hoping for harder ones ;) This is from the definition.

    f3[x_] := Piecewise[{{1 - x^2 , x < 0}, {1 + x^2, x > 0}}];
    FourierSeries[f3[x], x, 3]

![Mathematica graphics](http://i.stack.imgur.com/JPS7B.png)

And if you meant them to be different functions:

    f1[x_] := Piecewise[{{1 - x^2 , x < 0}, {0, True}}];
    f2[x_] := Piecewise[{{1 + x^2 , x > 0}, {0, True}}];
    FourierSeries[f1[x], x, 3]

![Mathematica graphics](http://i.stack.imgur.com/8FfCb.png)

    FourierSeries[f2[x], x, 3]

![Mathematica graphics](http://i.stack.imgur.com/wQM2d.png)


You can use the definition of the $c_k$ also by using `FourierParameters` to make it match the textbook you are using. So make sure to look at `FourierParameters` and adjust it as needed else you'll get different looking result from the textbook if the textbook does not use the default setting used by Mathematica.