model=a Exp[-b (x-c)^2]+d Sin[ω x+ϕ];
data=Table[{x,model/.{a->2,b->1,c->0,d->2,ω->0.67,ϕ->0.1}},{x,-5,5,.1}]+RandomReal[.25,101];

f1=FindFit[data,model,{a,b,c,d,ω,ϕ},x]

f2=FindFit[data,model,{a,b,{c,0},d,ω,ϕ},x]

Show[Plot[Evaluate[model/.{f1,f2}],{x,-5,5},PlotStyle->{Red,Blue}],ListPlot[data,PlotRange->All,PlotStyle->Gray]]