\documentclass[11pt]{book}
\usepackage{fancyhdr}
\usepackage{amssymb}
\usepackage{latexsym}
\usepackage{hyperref}
\usepackage{units}
\newcommand{\ds}{\displaystyle}
\newcommand{\testname}{Homework 4}
\newcommand{\testdate}{\today}
%		Problem
\newcounter{problemnumber}
\newcommand{\Problem}{\stepcounter{problemnumber}
       \item[\fbox{\parbox{.25in}{\hfil\theproblemnumber\hfil}}]}
\newcommand{\ProblemStar}{\stepcounter{problemnumber}
       \item[\fbox{\parbox{.25in}{$\star$\hfil\theproblemnumber\hfil}}]}
\newcommand{\Points}[1]{(#1 points) \ }
%		Examheader
\newcommand{\Examheader}{\setcounter{problemnumber}{0}
\centerline{\Large\bf \testname}

}
\lhead{\bf Advanced Calculus (MAA 4212)}
%\rhead{\bf Name: \rule{2in}{.2pt}}
\rhead{Due Wednesday 2/20}
\cfoot{}
\pagestyle{fancy}
%
%
\begin{document}
\thispagestyle{fancy}
\Examheader

\newcommand{\st}{\::\:}

%\bigskip\noindent\emph{Reminder: Midterm 2 is on Wednesday 3/20.}

%
%
%
%

\bigskip

\begin{enumerate}

\Problem Show that the function $f\st [0,1]\to\mathbb{R}$ defined by $f(x)=x^2$ is Riemann integrable. \emph{Your proof should use Lemma 11.11 and the identity
\[
	\sum_{j=1}^n j^2=\frac{n(n+1)(2n+1)}{6}.
\]}

\Problem Suppose $f\st [-1,1]\to\mathbb{R}$ takes nonnegative values. Show that if $f$ is Riemann integrable and continuous at $0$ and $f(0)>0$ then
\[
	\int_{-1}^1 f\,dx > 0.
\]

\end{enumerate}

\end{document}








