How do I represent $f(x) = \int_{-1}^{0} |x + t| dt, 0 \leq x \leq 2$ in an integrated form?

Question

Given the following function, how do I define it without the integral symbol?

$$f(x) = \int_{-1}^{0} |x + t| dt, 0 \leq x \leq 2$$

I don't understand how I determine when $x + t$ is positive and when it's negative when both $t$ and $x$ change.

Answer 1

Hints:

If $x\in [0,1]$, then $f(x)=\int_{-1}^{-x}-(x+t)dt+\int_{-x}^{0}(x+t)dt=\cdots$;

If $x\in [1,2]$, then $f(x)=\int_{-1}^{0}(x+t)dt=\cdots$