Suppose we want calculate the joint probability using double or triple integrals (depending on the problem) and a condition is defined as $P(x|y =0.5)$
Do we plug this value into the function and exclude integration?
We are assuming all the boundaries of integration for all random variables have been define: a<x<b , c<y<d, ....etc)
I think what you need is called marginalization. In this case, for the sum of two continuous rvs, $Y=X_1 +X_2$, $$ P(Y<y) = P(X_1+X_2<y) = \int_{-\infty}^{y}P(X_1+X_2<y|X_1=x_1)P(X_1 = x_1)dx_1 $$ Here $P(X_1 = x_1) = f_{X_1}(x_1)$ is the density of $X_1$.