\documentclass[oneside]{amsart}

% Boilerplate to put your name on every page
% This makes grading easier
\usepackage{authoraftertitle}
\usepackage{fancyhdr}
\pagestyle{fancy}
\fancyhead{}
\fancyfoot{}
\lhead{\MyAuthor}
\rhead{\thepage}

% Use letters in enumerated lists
\usepackage{enumitem}
\setenumerate[0]{label=(\alph*)}

% You can define abbreviations here
\newcommand{\problem}[1]{\par\noindent\textbf{Problem~#1}}
\newcommand{\answer}[1]{{\par\medskip\sffamily#1\par\medskip}}
\newcommand{\cl}{\mathop{\mathrm{cl}}\nolimits}
\newcommand{\R}{\mathbb{R}}
\newcommand{\N}{\mathbb{N}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\Q}{\mathbb{Q}}

\begin{document}

% Put your title, name, and the date here
\title{Homework 10}
\author{Your Name Here}
\date{April 27, 2020}

\maketitle


\problem{3.1.1.} If $f$ is a bounded function on $[a,b]$ and $P$ is any partition of $[a,b]$, show that $L(f,P)=-U(-f,P)$.

\answer{Type your answer here.}

\clearpage

\problem{3.1.4.} If $f:[a,b]\to\R$ is an increasing function, show that $f$ is integrable.

\answer{Type your answer here.}

\clearpage

\problem{3.1.7.} Show that if $a<b$, $f:[a,b]\to\R$ is a continuous function, $f(x)\geq 0$ for all $x$, and $\int_a^b f=0$, then $f(x)=0$ for all $x$ in $[a,b]$.

\answer{Type your answer here.}


\end{document}