Expanding the Fourier Series with odd extension

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My question wants me to derive the equality /4 = 1 - 1/3 + 1/5 - 1/7... using the Fourier Series:

4/ ∑ 1/(2n+1)sin((2n+1)x) = -1 if -1 < x < 0
                               1 if  0 < x < 1

To me it looks like the Fourier Sine expansion of f(x) = 1 with an odd extension, but where does the sin(nx) disappear to?