1. The problem is to find the limit $$\lim_{x \to 2} (x^2 - 6x + 1).$$\n\n2. The formula for limits of polynomial functions is straightforward: since polynomials are continuous everywhere, the limit as $x$ approaches a value is just the value of the polynomial at that point.\n\n3. Substitute $x = 2$ directly into the expression:\n$$2^2 - 6 \times 2 + 1 = 4 - 12 + 1.$$\n\n4. Simplify the expression:\n$$4 - 12 + 1 = -7.$$\n\n5. Therefore, the limit is $$\boxed{-7}.$$