TMUA 2020 · Paper 2 · Question 6

The function $f (x)$ is defined for all real values of $x$ .

Which of the following conditions on $f (x)$ is/are necessary to ensure that

\int_{- 5}^{0} f (x) d x = \int_{0}^{5} f (x) d x

Condition I: $f (x) = f (- x) for - 5 \leq x \leq 5$ Condition II: $f (x) = c for - 5 \leq x \leq 5, where c is a constant$ Condition III: $f (x) = - f (- x) for - 5 \leq x \leq 5$