Let f be a real valued continuous function on [0, 1] and $f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $. Then, which of the following points (x, y) lies on the curve y = f(x) ?

Question

Let f be a real valued continuous function on [0, 1] and $f(x) = x + \int\limits_0^1 {(x - t)f(t)dt} $.

Then, which of the following points (x, y) lies on the curve y = f(x) ?