\documentclass{article}

\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{amsthm}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{tikz}


\begin{document}
 Let $f(x)$ be the function graphed below.

\begin{center}
    \begin{tikzpicture}[scale=0.8]
    \draw[black, thick, <->] (-5.5, 0) -- (7.5, 0);
    \foreach \y in {-1, ..., 4}
    \draw[gray] (-5, \y) -- (7,\y);
    \draw[black, thick, <->] (0, -1.5) -- (0, 4.5);
    \foreach \x in {-5, ..., 7}
    \draw[gray] (\x, -1) -- (\x,4);
    
    \draw[black, very thick] (-4,2) -- (-2,0) arc (180:90:2);
    \draw[black, very thick] (0,1) -- (2,2) -- (3,2) arc (180:0:1) -- (6,0);
    \end{tikzpicture}
\end{center}

\begin{itemize}
    \item The part above $[-2, 0]$ is a quarter-circle with center (0,0) and radius $2$.
    \item The part above $[3,5]$ is a semi-circle with center (4,2) and radius 1. 
\end{itemize}

Come up with 4 different integration questions you could ask about the function $f$. These questions should all be of the form ``Compute $\int_a^b f(x)\ dx$'' where you get to pick the limits $a$ and $b$ (which should be integers). You could also combine multiple integrals into a single question. In addition, you should have two questions where the answer contains $\pi$, and two where it does not, and at least one of your answers should be negative. For each of your questions, provide a full solution. 
\end{document}