1. **Problem (a):** Evaluate $$\int_{-1}^0 \int_0^1 (x - y^2) \, dx \, dy$$. 2. **Formula and rules:** For iterated integrals, integrate the inner integral first with respect to $x$, then integrate the result with respect to $y$. 3. **Inner integral:** $$\int_0^1 (x - y^2) \, dx = \int_0^1 x \, dx - \int_0^1 y^2 \, dx = \left[\frac{x^2}{2}\right]_0^1 - y^2[x]_0^1 = \frac{1}{2} - y^2(1 - 0) = \frac{1}{2} - y^2$$ 4. **Outer integral:** $$\int_{-1}^0 \left(\frac{1}{2} - y^2\right) \, dy = \int_{-1}^0 \frac{1}{2} \, dy - \int_{-1}^0 y^2 \, dy = \left[\frac{y}{2}\right]_{-1}^0 - \left[\frac{y^3}{3}\right]_{-1}^0 = \left(0 - \frac{-1}{2}\right) - \left(0 - \frac{-1}{3}\right) = \frac{1}{2} - \left(-\frac{1}{3}\right) = \frac{1}{2} + \frac{1}{3} = \frac{3}{6} + \frac{2}{6} = \frac{5}{6}$$ **Final answer for (a):** $$\frac{5}{6}$$