Double Integration not working

edit

I am making a double integral interactive. However instead of giving my result for sin(xy) from x = 0 to x = 1 and y= 0 to y = 1 it gives integrate(-cos(2y)/y + 1/y,y,0,1).

 from sage.plot.plot3d.shapes import Box
x,y = var('x,y')
html("<h1>Double Integrator<h1>")
#permutations = ["dx dy","dy dx"]
@interact

def  interplay(function= input_box(sin(x*y)),lower_x_bound= input_box(0),upper_x_bound = input_box(1),lower_y_bound=input_box(0),upper_y_bound=input_box(1),dydx = checkbox(default = False)):



    try:    

          if dydx==False :              
                 prev = integral(function,x,lower_x_bound,upper_x_bound)
                 result = integral(prev,y,lower_y_bound,upper_y_bound)

                 q ="$\int_%s^{%s} \int_%s^%s %s \,dx\,dy = %s $" % (lower_y_bound, upper_y_bound,lower_x_bound,upper_x_bound,function,result)
                 # puts expressions inside latex
          else:
                result = integral(integral(function,y,lower_y_bound,upper_y_bound),y,lower_x_bound,upper_x_bound)
                #actually calculates integral
                q = "$\int_%s^{%s} \int_%s^%s %s \,dy\,dx = %s $" % (lower_x_bound,upper_x_bound,lower_y_bound,upper_y_bound,function,result)


         #if type(lower_x_bound)!=float or type(upper_x_bound)!=float or type(lower_y_bound)!= float or type(upper_y_bound)!= float :


          html("%s" %q)
    except:
        print(" "+"Please enter better bounds")





     #show(result)
html("<p> Created by Hans Gundlach </p>")