Why are these two integrals equal?

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$$\int_0^T\int_{-x}^{T-x} f(y) dy dx = \int_{-T}^T (T-|y|)f(y) dy$$

I'm so confused, but I can't reach from one side of equality to the other, please help me.

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Hint: Draw the set and use Fubini

EDIT: Here is the picture of the set.

enter image description here