Transreal arithmetic totalises real arithmetic by defining division by zero in terms of three definite, non-finite numbers: positive infinity, negative
infinity and nullity. We describe the transreal tangent function and extend continuity and limits from the real domain to the transreal domain. With this preparation, we extend the real derivative to the transreal derivative and extend proper integration from the real domain to the
transreal domain. Further, we extend improper integration of absolutely convergent functions from the real domain to the transreal domain. This demonstrates that transreal calculus contains real calculus and operates at singularities where real calculus fails
