f[x_] = x^4 - x - 10

g[x_] = x^2 + 6  x + 20

Plot[{f[x], g[x]}, {x, -10, 10}]

zeros = Solve[{f[x] == g[x]}, x]

N[zeros]

Integrate[g[x] - f[x], {x, -2.10655, 2.74462}]