data = {{-1, 0.98686}, {-0.9, 1.73109}, {-0.8, 
          3.01077}, {-0.7, 3.74048}, {-0.6, 4.29188}, {-0.5, 
          4.933}, {-0.4, 6.00188}, {-0.3, 5.91091}, {-0.2, 
          6.04255}, {-0.1, 5.81673}, {0, 5.07286}, {0.1, 5.25928}, {0.2, 
          4.77866}, {0.3, 4.31009}, {0.4, 4.09588}, {0.5, 3.89998}, {0.6, 
          4.10196}, {0.7, 3.73851}, {0.8, 4.39733}, {0.9, 3.94103}, {1. , 
          4.52398}}

ListPlot[data, PlotJoined -> True]

g[x_] = Fit[data, {1, x, x^2, x^3, x^4}, x]

Plot[g[x], {x, -1, 1}]