@MISC{INTEGRA6.MIZ,
  AUTHOR = {Endou, Noboru and Shidama, Yasunari and Yamazaki, Masahiko},
  TITLE = {Integrability and the Integral 
     of Partial Functions from $\Bbb R$ into $\Bbb R$},
  NOTE = {This work has been partially supported by the MEXT grant Grant-in-Aid for Young Scientists (B)16700156.},
  ACKNOWLEDGEMENT = {We would like to express our thanks to Prof. Yatsuka Nakamura.},
  SECTION1 = {Preliminaries},
  SECTION2 = {Integrability and the Integral of Partial Functions},
  SECTION3 = {Integrability on a Subinterval},
  SECTION4 = {Fundamental Theorem of Calculus},
  DAY = {17},
  MONTH = {November},
  YEAR = {2006},
  ADDRESS1 = {Gifu National College of Technology\\Gifu, Japan},
  ADDRESS2 = {Shinshu University\\Nagano, Japan},
  ADDRESS3 = {Shinshu University\\Nagano, Japan},
  SUMMARY = {In this paper, we showed the linearity of the
    indefinite integral
     $\int_a^b f dx$, the form of which was introduced in \cite{INTEGRA5.ABS}.
    In addition, we proved some theorems about the integral calculus on the
    subinterval of $[a,b]$. As a result, we described the fundamental
    theorem of calculus, that we developed in \cite{INTEGRA5.ABS}, by a
    more general expression.}}

