Help me please! Calculus - Theorem

Question

Evaluate  

Options:

1. 0
2. 1
3. 2
4. None of these

Answer 1

Let's think about what y = |x - 1| looks like:

The integral is the area under the curve (in this case the curve is a line) and the area from 0 to 2 is the same as 3 times the area from 1 to 2. The area from 1 to 2 is just the area of a triangle (1/2bh) which is 1/2*1*1 = 1/2. So the integral is 2 times 1/2 or 1 (answer 2)