$X_1$ and $X_2$ are samples from the homogenous distribution $[0,\theta]$ with $\theta > 0$ an unknown parameter. show that the density function of $Y= X_1 + X_2$ is given by:
$f_Y(y) = \left\{ \begin{array}{ll} \frac{y}{\theta^2} \;\; 0 \leq y \leq \theta\\ \frac{2\theta-y}{\theta^2} \;\; \theta \leq y \leq 2\theta\\ 0 \;\; elsewhere \end{array} \right.$
My approach has been: $P(X_1 \leq y-X_2)= \int_0^{2\theta}(\int_0^{y-x_2} f(x_1)f(x_2)dx_1)dx_2 = \frac{y-x_2}{{\theta}^2}$ which is nowhere near what the question is suggesting. What am I doing wrong here?