Computing area between curves

Let us compute the area between the curves y = (e^x) and y = 5 sin x + 8x + 7

Plot[{Exp[x], 5 Sin[x]+8 x+7}, {x,-3, 3.7}]

To find the points of intersection, we use FindRoot:

f[x_]=Exp[x]

g[x_]=5 Sin[x]+8 x+7

FindRoot[ f[x]-g[x], {x, -1}]

Here we have used x = -1 as a "seed" since we know that one root lies between -1 and 0.

FindRoot[ f[t]-g[t], {t, 3}]

Here we have used t = 3 as a "seed" since we know that one root lies between 3 and 4.

a=-0.49968948

b = 3.50437387

Area=NIntegrate[g[x]-f[x], {x,a, b}]