Find the area of two functions in wolfram mathematica

Question

I am having problems with drawing the area which is between two curves f(X)=-(x-2)^2+4 and g(x)=x/x+1 which says that the area is in the FIRST quadrant. Then to calculate the area of the area.Here is my code in wolfram mathematica.

f[x_] = -(x - 2)^2 + 4;
g[x_] = x/x + 1;
Plot[f[x] - g[x], {x, , }]
Integrate[f[x]-g[x],{x,,}]

.Thank you

Answer 1

f[x_] := -(x - 2)^2 + 4
g[x_] := x/x + 1
Plot[{f[x], g[x]}, {x, -1 , 5}]

sol = NSolve[f[x] == g[x], x]

{{x -> 0.585786}, {x -> 3.41421}}

{a, b} = x /. sol

{0.585786, 3.41421}

Integrate[f[x] - g[x], {x, a, b}]

3.77124