How to find f(x) using data interpolated using cubic spline interpolation

I have a set of values, x and y (f(x)), in a tabular form. I have used cubic spline interpolation to fit the data. i got the coefficients of the cubic spline interpolation for the interval [x0, xn]. How can i find the total equation of the function f(x) using the coefficients. Instead of finding cubic spline s(x) for a single interval, i need to find out the function for the whole interval. Like in polynomial interpolation, p(x)=p1x3+p2x2+p3x+p4,. The equations i have used in given below. Please help me on this.

The spline function s(x) on the interval [xl, xr] is defined by

s(x) = a0 + a1*(x-xl) + a2*(x-xl)^2 + a3*(x-xl)^3

With x in the interval [xl , xr].

For example, s (x) is defined in the interval [0, 0.0461], with coefficients a3=0.4891, a2=-0.09, a1=0.003 and a0=0.02, by the expression s(x) = 0.02+ 0.0031*(x-0) - 0.09*( x-0)^2 + 0.4891*( x-0)^3 s' (x) = 0.0031-0.1824*x+1.4673*x^2 s'' (x) = -0.1824 +2.9346*x Substituting the values s (0)= 0.02, s'(0)= 0.0031, s''(0)= -0.1824 s (0.0461)= 0.02, s'(0.0461)= -0.0022, s''(0.0461)= -0.0471