I'm not quite sure if my lower and upper bound for the following function are correct.

$\displaystyle f(y) = \left\{ \begin{array}{rcl}

2(1-y) & \mbox{for} & 0 \leq y \leq 1 \\

0 & \mbox{for} & \mbox{other}

\end{array}\right.$

Where $\displaystyle U_1 = 2Y-1$

$\displaystyle P(Y \leq \frac{u+1}{2}$

where $\displaystyle -1 \leq u \leq 1$

would it be:

$\displaystyle \int_0^{\frac{u+1}{2}}f(y) \ dy?$