Odd / Even integrals My textbook doesn't really have an explanation for this so could someone explain this too me. 
If f(x) is even, then what can we say about: $$\int_{-2}^{2} f(x)dx$$
If f(x) is odd, then what can we say about $$\int_{-2}^{2} f(x)dx$$ 
I guessed they both are zero? For the first one if its even wouldn't this be the same as $$\int_{a}^{a} f(x)dx = 0$$
Now if its odd f(-x) = -f(x). Would FTOC make this zero as well? 

Start by splitting the integral into two pieces, the part over negatives values of $x$ and the part over positive values.
$$ \int_{-2}^{2} f(x)\,dx = \int_{-2}^{0} f(x)\,dx + \int_{0}^{2} f(x)\,dx$$
From here you can apply the definition of an even or odd function
