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<div><span class="kw">theorem </span><a NAME="T1"><span class="comment"><font color="firebrick">:: INTEGR1C:1</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">f</font>, <font color="Olive" title="b2">g</font> being   <a href="partfun1.html#NM1" title="PARTFUN1:NM.1">PartFunc</a> of <a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a>,<a href="numbers.html#K2" title="NUMBERS:func.2">COMPLEX</a><br/>  for <font color="Olive" title="b3">C</font> being   <a href="integr1c.html#NM1" title="INTEGR1C:NM.1">C1-curve</a>  st  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b1">f</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <font color="Olive" title="b3">C</font> <a href="tarski.html#R1" title="TARSKI:pred.1">c=</a>  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <font color="Olive" title="b2">g</font> &amp; <font color="Olive" title="b1">f</font> <a href="integr1c.html#R1" title="INTEGR1C:pred.1">is_integrable_on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b2">g</font> <a href="integr1c.html#R1" title="INTEGR1C:pred.1">is_integrable_on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b1">f</font> <a href="integr1c.html#R2" title="INTEGR1C:pred.2">is_bounded_on</a> <font color="Olive" title="b3">C</font> &amp; <font color="Olive" title="b2">g</font> <a href="integr1c.html#R2" title="INTEGR1C:pred.2">is_bounded_on</a> <font color="Olive" title="b3">C</font> holds <br/> <a href="integr1c.html#K3" title="INTEGR1C:func.3">integral</a> (<span class="p1">(<span class="default"><font color="Olive" title="b1">f</font> <a href="valued_1.html#K2" title="VALUED_1:func.2">+</a> <font color="Olive" title="b2">g</font></span>)</span>,<font color="Olive" title="b3">C</font>) <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a> <span class="p1">(<span class="default"><a href="integr1c.html#K3" title="INTEGR1C:func.3">integral</a> (<font color="Olive" title="b1">f</font>,<font color="Olive" title="b3">C</font>)</span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p1">(<span class="default"><a href="integr1c.html#K3" title="INTEGR1C:func.3">integral</a> (<font color="Olive" title="b2">g</font>,<font color="Olive" title="b3">C</font>)</span>)</span></div></div>
