Hello everyone

I have the following problem. I need to find a function, say $\displaystyle f(x)$, that maximizes

$\displaystyle \int_{a}^{b}u(x)f(x)dx$, where $\displaystyle u(x)$ is the square of the cumulative distribution function of the standard normal minus one half, i.e. $\displaystyle u(x)=(\phi(x)-1/2)^2$.

The maximisation problem does not have prespecified boundary values for $\displaystyle a$ and $\displaystyle b$, and is subject to the constraint $\displaystyle \int_{a}^{b}f(x)dx = 1$

any help is really precious

thanks

Lorenzo