Since both 2x-1 and x^2 are polynomials (a line is both linear and polynomial) they are continuous on their domain. The problem is do they link up nicely. That is, is f(x) continuous at x=1.
f(x) is continuous at x=1 if the following conditions are met:
1a) The left hand limit at x=1 exist
1b) The right hand limit at x=1 exist.
2) Both of the limits in 1 are equal. Say the common limit is L
3) f(1) = L
Have all these conditions been met in your example. If not, then the function f(x) is not continuous at x=1. Which conditions, if any, have not been met??