Line integrals of scalar functions

Suppose we have a scalar field $f(x, y) = x^2 + y^2$f, left parenthesis, x, comma, y, right parenthesis, equals, x, squared, plus, y, squared and a curve $C$C that is parameterized by $\alpha(t) = (t, (t - 2)^2)$alpha, left parenthesis, t, right parenthesis, equals, left parenthesis, t, comma, left parenthesis, t, minus, 2, right parenthesis, squared, right parenthesis for $-2 < t < 1$minus, 2, is less than, t, is less than, 1.