Probability of multiple distributions

I have a question concerning the calculation of the probability of an event among multiple probability distributions. Let's say we have two continuous probability distributions $$D_1$$ and $$D_2$$, given by the functions $$f_1$$ and $$f_2$$, respectively, and their two random variables $$X_1$$ and $$X_2$$, belonging to $$D_1$$ and $$D_2$$, respectively. I would like to know how to calculate the probability of $$x_1 + x_2 > T$$, i.e., $$P(x_1 + x_2 > T)$$.

Thanks for your attention, case my notations are not understandable or any point is not clear, please let me know.

ps.: I am not a mathematician.

Plot the product of the two (independent) distributions as a function of $$X_1$$ and $$X_2$$. Then consider the criterion line (plane) $$X_1 + X_2 = T$$.
The probability $$P(X_1 + X_2 \geq T)$$ is thus the integral of the joint probability above that plane (to the upper right) divided by the integral over the whole space (i.e., the normalization).
$$P(X_1 + X_2 \geq T ) = \frac{\int\limits_{x=0}^\infty \int\limits_{y = \max[0,T-x]}^\infty D_1(x) D_2(y)\ dx\ dy}{\int\limits_{x=0}^\infty \int\limits_{y = 0}^\infty D_1(x) D_2(y)\ dx\ dy}$$