Đáp án

\( x f'(x) - x^2 e^x = f(x) \iff \frac{x f'(x) - f(x)}{x^2} = e^x \).

\(\left( \left( \frac{f(x)}{x} \right)' = \frac{x f'(x) - f(x)}{x^2}\right) \)

\(\implies \left( \frac{f(x)}{x} \right)' = e^x \implies \frac{f(x)}{x} = e^x + C \).

\( f(1) = e  \implies C = 0 \implies f(x) = x e^x \).

\( I =  \int_1^2 x e^x \, dx = e^2 \implies \boxed{C} \).