Finding the Joint and Density Functions for Independent Uniform Random Variables

[mlarson9000]

Homework Statement

Let X and Y be independent uniform (0,1) random variables.

a. find th ejoint density of U=X, V=X+Y.

b. compute the density funciton of V.

Homework Equations

The Attempt at a Solution

Part a. is not a problem. I don't understand how the bounds for part b. are set up. The book says: for 0<V<1, fv(v)=\int_{o}^{v}du
and for 1\leqv\leq 2: \int_{v-1}^{1}du

Could someone explain this to me?

 

[mlarson9000]

Could somebody explain this in English?