Sum of Two Independent Random Variables (uniform)

Suppose X and Y are Uniform(-1, 1) such that X and Y are independent and identically distributed. What is the density of Z = X + Y?

Here is what I have done so far (I am new to this forum, so, my formatting is very bad). I know that

fX(x) = fY(x) = 1/2 if -1<x<1 and 0 otherwise

The density of Z will be given by

fZ(z)= integral fX(z-y)fY(y)dy bounds of integration from -infinity to infinity

fY(y) = integral 1/2 if -1<y<1 and 0 otherwise

So,

fZ(z) = (1/2)fX(z-y)dy (bounds of integration -1 to 1)

The integrand = 1/2 if -1<z-y<1 or z-1<y<z+1

or 0 otherwise

This is where I get stuck and not sure how to proceed. Thanks