I am assuming that question meant to say

#f(x)=3x^2 " for " -1 < x < 1; 0 " otherwise"#

Find the variance?

#Var = sigma^2 = int (x-mu)^2f(x) dx#

Expand:

#sigma^2 = intx^2f(x) dx-2mucancel(intxf(x)dx)^mu+mu^2cancel(intf(x) dx)^1#

#sigma^2 = intx^2f(x) dx-2mu^2+mu^2=intx^2f(x)dx - mu^2#

substitute

#sigma^2 = 3int_-1^1 x^2 *x^2dx -mu^2 = sigma_0^2+mu^2#

Where, #sigma_0^2=3int_-1^1 x^4dx# and #mu=3int_-1^1 x^3dx#

So let's calculate #sigma_0^2 " and " mu#

by symmetry #mu=0# let see:

#mu=3int_-1^1 x^3dx = [3/4x^4]_-1^1 = 3/4[1-1]#

#sigma_0^2=3int_-1^1 x^4dx=3/5[x^5]_-1^1 = 6/5#