Defective Item

Chef has a container that opens from both ends and contains $N$ items numberd from $1$ to $N$. He realizes that one item whose value is $x$ is defective and wants to remove it from the container. To remove an item Chef has to start from one end and take out each item till the defective piece is no more there. Work done will be the sum of values of items taken out in the process (including the defe