Question

Let \[ f:[0,1]\rightarrow\mathbb R \] be a function defined by \[ f(x)+f(1-x)=1. \] Then \[ \int_0^1 f(x)\,dx= \ ? \]

• A. 0
• B. 1
• C. 2
• D. \(\frac12\)

Hint:

If a function satisfies \[ f(x)+f(a-x)=k, \] then \[ \int_0^a f(x)\,dx=\frac{ka}{2}. \] This is a standard result.

Answer 1

The Correct Option is D