well the curve is symmetrical abt y axis meeting it at (0, 1) and it exp decreases

let the pt of max area on x axis b x , y=1/e power x

 due 2 symmetry the area will be 2* area on + side of x axis.

if u draw a proper fig u can c dat area will be 2x*e^x

maximise it using calculus and get the ans