1. The problem is to determine whether the statement \n\n"If $$\int_{-1}^{1} f(x)\,dx = 0$$ then $$f(x)$$ is odd"\n\nis true or false.\n\n2. Recall the property of odd functions: for an odd function $$f(x)$$, $$f(-x) = -f(x)$$, and the integral of an odd function over symmetric limits is zero, i.e., $$\int_{-a}^{a} f(x)\,dx = 0$$.\n\n3. However, the converse of this property is not necessarily true. Just because $$\int_{-1}^{1} f(x)\,dx = 0$$ does not imply that $$f(x)$$ is odd. The integral could be zero if the positive and negative areas cancel out, even if the function itself is not odd.\n\n4. For example, a function that is neither purely odd nor even but integrates to zero over symmetric limits would serve as a counterexample.\n\n5. Therefore, the statement is \n\n**False**.