Hi,   
      
   with the assumption   
     $Assumptions = f \[Element] Reals && X \[Element] Reals   
   the integral   
     Integrate[Exp[(f + 1) x], {x, 1/2, X}]   
   improperly returns two(?) distinct "integral does not converge" messages,   
   while with no assumptions   
     $Assumptions = True   
   the same Integrate[...] returns the correct result without restriction on   
   conditions. (The returned result is valid for f different from -1; correct in   
   the limit where f goes to -1).    
      
   Would you estimate Mathematica behaves properly?   
      
   I observe the same phenomenon using    
    mathematica 9.0.1.0   
    mathematica 10.0.0.0   
    mathematica 10.0.2.0   
   on linux x86 (64bits)   
    Linux 3.16.0-4-amd64 #1 SMP Debian 3.16.7-ckt2-1 (2014-12-08) x86_64 GNU/Linux   
      
   Best,   
      
   Vivien   
      
   PS, adding the condition f ≠ 1 provides a correct answer   
     $Assumptions = f \[Element] Reals && X \[Element] Reals && f != -1   
   It thus seems Mathematica does not correctly determine the integrability   
   condition... of an exponential.   
      
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