Theorems on Integrability

Theorem 1

Suppose is bounded, and integrable on for all . Then is integrable on . Also valid for the other end.

Proof Hint

• Isolate a partition on the required end.
• Choose or such that where is an upper or lower bound.

Theorem 2

Suppose is bounded, and continuous on for all . Then is integrable on . Also valid for the other end.