Final answer:
To evaluate the integral, use the Fundamental Theorem of Calculus and find the values of G(1), H(1), G(2), and H(2).
Step-by-step explanation:
To evaluate the integral ∫2 to 1 f(x)dx = -2, we need to use the Fundamental Theorem of Calculus. According to the theorem, if F(x) is an antiderivative of f(x), then ∫a to b f(x)dx = F(b) - F(a). Since ∫2 to 1 f(x)dx = -2, we can rewrite it as F(1) - F(2) = -2.
Let's say F(x) = G(x) - H(x), where G(x) is an antiderivative of f(x) from 1 to x, and H(x) is an antiderivative of f(x) from 2 to x. We can rewrite F(1) - F(2) as (G(1) - H(1)) - (G(2) - H(2)).
Plugging in the given information, we get G(1) - H(1) - G(2) + H(2) = -2. Therefore, to evaluate the integral, we need to find the values of G(1), H(1), G(2), and H(2).