find the total area enclosed by the functions f and g

f(x) = \(x^{2}\)-3x+2 g(x) = -3x + 3

# create functions f and g
f <- function(x) {x^2-3*x+2}
g <- function(x) {-3*x+3}

# draw both functions f and g
curve(expr=f, from = -3, to = 3)
curve(expr=g, from = -3, to = 3, add = T)

# find lower intersection
rt <- uniroot(function(x)  f(x) - g(x)  , interval = c(-3,0), tol=0.00001) 
rt$root
## [1] -1
# find upper intersection
rt <- uniroot(function(x)  f(x) - g(x)  , interval = c(0, 3), tol=0.00001) 
rt$root
## [1] 1
# f area between -1 and 1
f_area <- integrate(f, lower = -1, upper = 1)
# g area between -1 and 1
g_area <- integrate(g, lower = -1, upper = 1)

# area in between
g_area$value - f_area$value
## [1] 1.333333