1. The problem is to find the normalizing constant $c$ such that $$\int_{-\infty}^{\infty} c e^{-x^2/2} \, dx = 1.$$\n\n2. We use the fact that the integral of the Gaussian function without the constant is known: $$\int_{-\infty}^{\infty} e^{-x^2/2} \, dx = \sqrt{2\pi}.$$\n\n3. Since $c$ is a constant multiplier, it can be factored out of the integral: $$c \int_{-\infty}^{\infty} e^{-x^2/2} \, dx = c \sqrt{2\pi}.$$\n\n4. We want this to equal 1, so set up the equation: $$c \sqrt{2\pi} = 1.$$\n\n5. Solve for $c$: $$c = \frac{1}{\sqrt{2\pi}}.$$\n\n6. This result uses the improper integral of the Gaussian function over the entire real line, which converges to $\sqrt{2\pi}$.\n\nFinal answer: $$c = \frac{1}{\sqrt{2\pi}}.$$