The inner integral is with respect to x, so we treat y as a constant. The integral of a constant with respect to x is the constant times x. So, we have:
$$\int_{0}^{4-y^{2}} y d x = y \cdot x \Big|_{0}^{4-y^{2}} = y(4-y^{2}) - y(0) = 4y - y^{3}$$
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