2 dependent random variables with Covariance = 0

I'm new to proofing and advanced maths, so I need help with this task:

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given two random variables X & Y, where:

Y = -X if -c <= X <= c
Y = X if X is not in the interval [-c,c]

show that c can be chosen so that Cov(X,Y) = 0, but that the two random variables are dependent.
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I can see the variables are clearly dependent, but I find it really hard to find the c value. Can anyone help?

Let's see, you want E(XY)=E(X)E(Y) where