Finding the probability of a joint density

Given the joint density of two random variables $$X$$ and $$Y$$,

$$f_{XY}(x,y)=2e^{-(x+y)}$$ for $$0

How do I compute $$P(Y<1|X=1)$$?

I know the conditional probability formula is:

$$P(Y<1|X=1)=\frac{P(X=1,Y<1)}{P(X=1)}=\frac{\int\int2e^{-(x+y)}dydx}{\int\int2e^{-(x+y)}dydx}$$

However, I'm unsure about the bounds of the integral

The PDF tells us that $$X a.s. so that $$P(Y<1\mid X=1)=0$$.