1. **Problem:** Calculate the definite integral $$\int_0^1 (3 - 2x) \, dx$$ 2. **Formula:** The definite integral of a function $f(x)$ from $a$ to $b$ is given by $$\int_a^b f(x) \, dx = F(b) - F(a)$$ where $F(x)$ is the antiderivative of $f(x)$. 3. **Step 1:** Find the antiderivative of $3 - 2x$. $$\int (3 - 2x) \, dx = 3x - x^2 + C$$ 4. **Step 2:** Evaluate the antiderivative at the bounds 1 and 0. $$F(1) = 3(1) - (1)^2 = 3 - 1 = 2$$ $$F(0) = 3(0) - (0)^2 = 0$$ 5. **Step 3:** Calculate the definite integral. $$\int_0^1 (3 - 2x) \, dx = F(1) - F(0) = 2 - 0 = 2$$ **Final answer:** $$2$$