Question Detail

Option A is correct: the definite integral over an interval of zero length is always zero. Option B is trivially correct, stating an identity. Option D is correct: it's a fundamental comparison property of definite integrals, stating that if one function is always less than or equal to another over an interval, its integral will also be less than or equal to the other's integral. Option C is incorrect. The property states that the absolute value of an integral is less than or equal to the integral of the absolute value: |∫ab f(x)dx| ≤ ∫ab |f(x)|dx. For example, if f(x) = -1 on [0,1], then ∫01 (-1)dx = -1, but ∫01 |-1|dx = 1. So, -1 ≠ 1.